Geometry parallel lines proofs worksheet

4.9. (8) $1.50. PDF. There are 7 practice proofs for parallel lines, ranging in difficulty from 3 steps to 8 steps. The proofs also include practice with the Theorem "If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line."

Geometry parallel lines proofs worksheet. Utilizing Parallel Lines in Proofs Reasons 1) Given 2) Given 3) If parallel lines cut by transversal, then altemate angles are conguent ... Geometry Applications : EXAMPLE: Ifquadfi1atera1PLAY has angles P: 59 degrees L: 37 degrees A: 143 degrees Y: 121 degrees Which sides are parallel? Sketch the figure.

Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. There are over 85 topics in all, from multi-step equations to constructions. Suitable for any class with geometry content. Designed for all levels of learners, from remedial to advanced. Topics.

Notes: PROOFS OF PARALLEL LINES Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 164 EXAMPLE 2: Given: r ‖s m ‖ l Prove: m 5 + m 11 = 180° Fill in any missing statements or reasons to complete the proof. Statements Reasons 1. 1. Given 2. 5 & 9 are supplementary. 2. 3. 3. Definition of supplementary angles 4. 4. 5. 5.of two parallel lines, then it is perpendicular to the other line. If h k and j ⊥ h, then j ⊥ k. Proof Example 2, p. 150; Question 2, p. 150 Theorem 3.12 Lines Perpendicular to a Transversal Theorem In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. If m ⊥ p and n ⊥ p, then m n.Parallel provides the same types of services a school district or parent has used in the past, just in a telehealth setting. If a kid is having trouble at school, one of the standa...Software for math teachers that creates custom worksheets in a matter of minutes. Try for free. Available for Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus.Worksheets are Proofs with perpendicular lines, Honors geometry chapter 3 proofs involving parallel and, Geometry beginning proofs packet 1, Parallel and perpendicular lines, Geometry proofs and postulates work, Geometry proof practice answers, Math work, Chapter 3 parallel and perpendicular lines. *Click on Open button to open and …

4.9. (8) $1.50. PDF. There are 7 practice proofs for parallel lines, ranging in difficulty from 3 steps to 8 steps. The proofs also include practice with the Theorem "If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line." Geometry Worksheet - Proofs Worksheet Proving Lines Parallel by Word of Math. 2 Ratings. View Preview. Grade Levels. 7th - 10th. Subjects. Math, Geometry. Resource …3.3 Prove Lines are Parallel FCA 5 #1-11 Hw: Proving Lines Parallel Worksheet Extra Practice 3.3 Proving Lines Parallel 3.3 Prove Lines are Parallel FCA 6 ALL Hw: p 151 # 41* (use paragraph form), pp 160 - 161 # 31*, 36, 37 **You will be turning in # 41, 31** FCA 3.3 Prove Lines are Parallel ALL 7 Extra Proof PracticeUtilizing Parallel Lines in Proofs Reasons 1) Given 2) Given 3) If parallel lines cut by transversal, then altemate angles are conguent 4) Transitive property 5) If base angles are congruent, then triangle is isosceles AEK BED 1) 2) 5) ABE is isosceles BED EBA BAE BAE or Recognizing the altemate interior angles... Example: Given: Prove: Circle E©e Z2t0 h1Z1 k qK UuNtraS ZSZo HfRtqw na cr 6e5 eL KLSC Z.C U 3ASl1lL Qr3i Rguh Nt2s E srIe Ys0e Ir XvYePd2. 7 Z xMkakdJe O lw aiItWh9 tI xnvf 9iCnxi Gtne s LGKecoTmTeZt hrxy G.0 Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Parallel Lines and Transversals Date_____ Period____

Pre-made digital activities. Add highlights, virtual manipulatives, and more. 1.and have no points in common. and are parallel. 2.and have only one point in common. and intersect. 3.and have all points in common. and are the same line. These three possibilities can also be stated in the following postulate: Postulate 9.1Two distinct coplanar lines are either parallel or intersecting. CD. Title: geo_3.3_proofs0001.pdf Author: JBRESLOW Created Date: 10/21/2014 1:41:45 PMLines Postulates And Theorems Name Definition Visual Clue. Postulate Through a point not on a given line, there is one and only one line parallel to the given line. Alternate Interior Angles Theorem If two parallel lines are intersected by a transversal, then alternate interior angles are equal in measure.Proofs involving parallel lines I. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more.Triangle And Parallel Lines. Displaying all worksheets related to - Triangle And Parallel Lines. Worksheets are 7 proportional parts in triangles and parallel lines, Name geometry unit 2 note packet triangle proofs, Geometry part 1 lines and angles, Ms work 132 153 geometry 06, Parallel lines parallel, Proving lines parallel, Parallel ...

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Unit test. Test your understanding of Congruence with these NaN questions. Start test. Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms. Lines and angles worksheets are perfect for students to learn and practice various problems about different angle concepts and situations. These worksheets are a great resource for students who wish to grow and improve their skills in angles. Lines and angles worksheets consist of concepts like naming angles, lines, classifying angles ...Triangle And Parallel Lines. Displaying all worksheets related to - Triangle And Parallel Lines. Worksheets are 7 proportional parts in triangles and parallel lines, Name geometry unit 2 note packet triangle proofs, Geometry part 1 lines and angles, Ms work 132 153 geometry 06, Parallel lines parallel, Proving lines parallel, Parallel ...2_test_honors.tst. Download File. 3.1_pairs_of_lines_and_angles.pdf. Download File. 3.2_parallel_lines_and_transversals.pdf.

Parallel lines and transversals worksheets can help students to learn about angles formed by parallel lines cut by a transversal. Parallel lines and transversals worksheets will help kids in solving geometry problems. Some real-life examples of parallel lines cut by a transversal are zebra crossing on the road, road and railway crossing ...Kuta Software - Infinite Geometry Name_____ Parallel Lines and Transversals Date________________ Period____ Identify each pair of angles as corresponding, … Displaying all worksheets related to - Parallel Line Proofs. Worksheets are Parallel lines, Using parallel lines in proofs, Honors geometry chapter 3 proofs involving parallel and, Work section 3 2 angles and parallel lines, Chapter 3 parallel and perpendicular lines, Geometry beginning proofs packet 1, Geometry proofs and postulates work, Geometry chapter 2 reasoning and proof. Geometry unit 3 parallel lines solving equations worksheetParallel lines worksheet proving unit lesson followers Parallel geometry line wikipedia transversalParallel angles lines worksheet geometry. Parallel perpendicular angles worksheet formed corresponding plzzParallel lines proofs practice worksheet for 8th …Section 3.2 Parallel Lines and Transversals 133 Using Properties of Parallel Lines Find the value of x. a b 4 115° (x + 5)°SOLUTION By the Vertical Angles Congruence Theorem (Theorem 2.6), m∠4 = 115°.Lines a and b are parallel, so you can use the theorems about parallel lines. m∠4 + (x + 5)° = 180° Consecutive Interior Angles Theorem 115° + (x + …Flip. Space. Created by. d_getman. vocab for proof and parallel lines. vocab for proof and parallel lines Learn with flashcards, games, and more — for free.ÐÏ à¡± á> þÿ ý ÿ þÿÿÿõ ö ÷ ø ù ú û ü ø ...If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. If two lines are parallel to the same line, then they are parallel to each other. Study with Quizlet and memorize flashcards containing terms like Converse, Parallel Lines, Transversal and more. Parallel line proofsConverse parallel line proofsIncludes:- modified proofs with either the statements or reasons missing.- modified proofs with reasons missing- complete proofs with reasonsCongruent Triangle Proofs© 2018 Yevgeniy Sidorevich, "Pi Classroom"Products by Yevgeniy Sidorevich (Pi Classro... Independent Practice: PROOFS OF PARALLEL LINES NAME: DATE: PERIOD: Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 167 For # 1-3, given a ‖ b, state the postulate or theorem that justifies each conclusion. 1. 1 is supplementary to 8 because given _____ 2. 4 5 2 7 becauseParallel lines worksheet answers proving proofs math activity proof sites geometry chessmuseum related posts teacherspayteachersParallel lines proofs worksheet answers / proving lines parallel 1 Geometry worksheet parallel lines proving proofs pdf printableParallel lines proofs practice worksheet lesson curated reviewed …

If two lines are perpendicular to the same line, they are parallel to each other and will never intersect. Advertisement Welders and carpenters use all sorts of tools to set things...

912.G-GPE.2.5 - Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line ...Definitions, Postulates and Theorems. Page 5 of 11. Triangle Postulates And Theorems Name Definition Visual Clue. Angle-Angle (AA) Similarity Postulate If two angles of one triangle are equal in measure to two angles of another triangle, then the two triangles are similar. Side-side-side (SSS) Similarity Theorem If the three sides of one ...Step 1: Read through the steps of the proof, making note of the given information (usually in "Step 1") and what it is we are asked to prove (usually in the last "Step"). Step 2: Identify which ...3. Parallel Lines can be a lifesaver. This is an old trick that you would be familiar with as well. Any parallel lines in the proof’s diagram mean that you would use one of the parallel-line theorems. Pass on this wisdom to help your children solve geometry proofs given in the geometry proofs list. 4. If-then logic is always goldParallel provides the same types of services a school district or parent has used in the past, just in a telehealth setting. If a kid is having trouble at school, one of the standa...Independent Practice: PROOFS OF PARALLEL LINES . 7. Given: . r. ‖. s. l. ‖. m. Prove: . . 6. . 14. Use the following word bank to complete the proof. 1. 2. 5. 6 r. 3. 4. 7 8. 15. 16. …Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. There are over 85 topics in all, from multi-step equations to constructions. Suitable for any class with geometry content. Designed for all levels of learners, from remedial to advanced. Topics.G.6.4: Prove and use theorems involving the properties of parallel lines cut by a transversal, similarity, congruence, triangles, quadrilaterals, and circles; Geometry - …Title: geo_3.3_proofs0001.pdf Author: JBRESLOW Created Date: 10/21/2014 1:41:45 PMThe symbol ∥ means “is parallel to.”. When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs. A transversal is a line that intersects two or more coplanar lines at distinct points. The special angle pairs formed by parallel lines and a transversal are congruent, supplementary, or ...

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There are several angle relationships of which students should be aware. Complementary angles are two angles that together form a 90 degree angle; supplementary angles are two angles that together form a 180 degree angle; and explementary angles are two angles that together form a 360 degree angle.Vertical angles are found at line intersections; angles …of two parallel lines, then it is perpendicular to the other line. If h k and j ⊥ h, then j ⊥ k. Proof Example 2, p. 150; Question 2, p. 150 Theorem 3.12 Lines Perpendicular to a Transversal Theorem In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. If m ⊥ p and n ⊥ p, then m n.Section 3.3 Proving Lines Parallel. G.1.1: Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning; G.6.4: Prove and use theorems involving the properties of parallel lines cut by a transversal, similarity, congruence, triangles, quadrilaterals, and circles;You have already learned how to that certain angle pairs are congruent if you have parallel lines. Now you will have to use the same logic to work backwards to prove that lines are parallel. Use the following diagram for each proof. n Part 1 – “Mini Proofs” – Proving Lines are Parallel in 2 Steps 1. Given: 1 # 8 Prove: m || n 2. Given: 1 5 Flip. Space. Created by. d_getman. vocab for proof and parallel lines. vocab for proof and parallel lines Learn with flashcards, games, and more — for free. The following proof of Theorem 3-12 relies on the idea that through a point not on a given line you can draw a line parallel to the given line. Proof of Theorem 3-12 Given: #ABC Prove: m&A + m&B + m&3 = 180 Proof: By the Protractor Postulate, you can draw so that m&1 = m&A.Then, &1 and &A are congruent alternate interior angles, so 6 . Unit test. Test your understanding of Congruence with these NaN questions. Start test. Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms. Corresponding angles are easy to find once you know what to look for. Advertisement Geometry is packed with terminology that precisely describes the way various points, lines, surf...Resources tagged with: Angles - points, lines and parallel lines Types All types Problems Articles Games Age range All ages 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level There are 70 NRICH Mathematical resources connected to Angles - points, lines and parallel lines , you may find related items under Angles, polygons, and geometrical proof . This free geometry worksheet requires the use of the properties of parallel lines including the Alternate Interior Angle Theorem, Corresponding Angles Theorem, and the Same-Side Interior Angle Theorem and their converses. Problems include the completion proofs and finding the values of missing angles to make a pair of lines parallel. To prove ... Triangle And Parallel Lines. Displaying all worksheets related to - Triangle And Parallel Lines. Worksheets are 7 proportional parts in triangles and parallel lines, Name geometry unit 2 note packet triangle proofs, Geometry part 1 lines and angles, Ms work 132 153 geometry 06, Parallel lines parallel, Proving lines parallel, Parallel ...These worksheets help students learn the converse of the parallel lines as well. Benefits of Proving Lines Parallel Worksheets. Proving lines parallel worksheets are a great resource for students to practice a large variety of parallel lines questions and problems. These math worksheets are supported by visuals which help students get a crystal ... ….

Unit test. Test your understanding of Congruence with these NaN questions. Start test. Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms. THOUGHT PROVOKING Draw a diagram of at least two lines cut by at least one transversal. Mark your diagram so that it cannot be proven that any lines are parallel. Then explain how your diagram would need to change in order to prove that lines are parallel. PROOF In Exercises 33–36, write a proof.Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. There are over 85 topics in all, from multi-step equations to constructions. Suitable for any class with geometry content. Designed for all levels of learners, from remedial to advanced. Topics.parallel lines and transversals -Prove that two lines are parallel Worksheet 3.2 -3.3 3 3.4 Find and Use Slopes of Lines -Find slopes of lines -Use slopes to identify parallel and perpendicular lines Worksheet 3.1 -3.4 Study for Quiz 4 QUIZ 3.1-3.4 3.5 Write and Graph Equations of Lines -Demonstrate mastery -Wr ite equations of lines inWhen two lines are intersecting 7. Definition of an angle bisector Results in two angles being congruent 3. Right Angles are Congruent When you are given right triangles and/or a square/ rectangle 8. Definition of a perpendicular bisector Results in 2 congruent segments and right angles. 4. Alternate Interior Angles of Parallel Lines are congruentUnit test. Test your understanding of Congruence with these NaN questions. Start test. Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms.There are all sorts of ways to bug-proof your home. Check out this article from HowStuffWorks and learn 10 ways to bug-proof your home. Advertisement While some people are frighten...Unit test. Level up on all the skills in this unit and collect up to 1,900 Mastery points! In this topic, we'll learn about special angles, such as angles between intersecting lines and triangle angles. Next, we'll learn about the Pythagorean theorem. Finally, we'll find volume of curved 3D shapes like spheres, cones, and cylinders. Geometry parallel lines proofs worksheet, Pre-made digital activities. Add highlights, virtual manipulatives, and more., When we feel love and kindness toward others it not only makes others feel loved and cared for, it helps us al When we feel love and kindness toward others it not only makes others..., 18) Even if the lines in question #16 were not. Any value other than 8. Ideally 0 ≤ x ≤ 10. parallel, could. No, that would make the angles 189° and 206°. Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com., Independent Practice: PROOFS OF PARALLEL LINES NAME: DATE: PERIOD: Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 167 For # 1-3, given a ‖ b, state the postulate or theorem that justifies each conclusion. 1. 1 is supplementary to 8 because given _____ 2. 4 5 2 7 because, Parallel lines and transversals. Proving lines parallel. Points in the coordinate plane. The Midpoint Formula. The Distance Formula. Parallel lines in the coordinate plane. …, 912.G-GPE.2.5 - Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line ... , Perpendicular lines parallel math worksheet worksheets geometry grade fourth 4th line activities gr4 angles common core intersecting identifying standards mathsPerpendicular parallel worksheet intersecting lines line answers math practice excel db circuits symbols please Parallel perpendicular neither answers equations odd …, 25) Fill in the blank so that the lines are not parallel: Line A goes through Line B goes through----- -----( , ) and ( , ) ( , ) and ( , ) Anything but 26) Write the equations of five lines that are parallel to y x Many answers. Ex: y x -2-Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com, Independent Practice: PROOFS OF PARALLEL LINES . 7. Given: . r. ‖. s. l. ‖. m. Prove: . . 6. . 14. Use the following word bank to complete the proof. 1. 2. 5. 6 r. 3. 4. 7 8. 15. 16. …, 3.3 Prove Lines are Parallel FCA 5 #1-11 Hw: Proving Lines Parallel Worksheet Extra Practice 3.3 Proving Lines Parallel 3.3 Prove Lines are Parallel FCA 6 ALL Hw: p 151 # 41* (use paragraph form), pp 160 - 161 # 31*, 36, 37 **You will be turning in # 41, 31** FCA 3.3 Prove Lines are Parallel ALL 7 Extra Proof Practice, Unit 6: Analytic geometry. 0/1000 Mastery points. Distance and midpoints Dividing line segments Problem solving with distance on the coordinate plane. Parallel & perpendicular lines on the coordinate plane Equations of parallel & perpendicular lines., Algebra I Worksheets Honors Geometry Honors Geometry Notes Honors Geometry Worksheets ... 3.4_proofs_with_perpendicular_lines.pdf: File Size: 200 kb: File Type: pdf: ... File Size: 116 kb: File Type: pdf: Download File. parallel_lines_poster_directions.pdf: File Size: 425 kb: File Type: pdf: Download File. 5.1_angles_of_triangles.pdf: File Size ..., 1.and have no points in common. and are parallel. 2.and have only one point in common. and intersect. 3.and have all points in common. and are the same line. These three possibilities can also be stated in the following postulate: Postulate 9.1Two distinct coplanar lines are either parallel or intersecting. CD. , Hand over this set of worksheets on Parallel and Perpendicular Lines to your students for teaching them to identify, draw and determine parallel and perpendicular lines. In addition to this, the set also contains practice worksheets on determining whether two lines are parallel or perpendicular, using points, slopes and equations., 10.2A Angles Formed by Two Straight Lines and a Transversal In the figure, a straight line EF intersects two other straight lines AB and CD. The straight line EF is called a transversal of AB and CD. The 8 angles formed are named according to their relative positions. Corresponding Angles Alternate Angles Interior Angles on the Same Side 1., 18) Even if the lines in question #16 were not. Any value other than 8. Ideally 0 ≤ x ≤ 10. parallel, could. No, that would make the angles 189° and 206°. Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com. , If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. If two angles are supplementary to the same angle or to congruent angles, then they are congruent., PARALLEL LINES AND PROOFS 1 worksheet / Page 1 of 5 (pg 3+ contain answers) FIGURE 1 NOTE: When proving a theorem, you may not use the theorem you are attempting to prove as a reason in the proof. 1. USING FIG 1: Prove “If the lines intersected by a transversal are parallel, then the alternate interior angles are congruent., Mac: Parallels, the popular Mac software that allows you to run Windows in a virtual environment on your Mac, has released an update that brings in support for Windows 10. Mac: Par..., Benefits of Parallel and Perpendicular Lines Worksheets. Parallel and perpendicular lines worksheets are helpful to improve the geometry skills of students. Practice exercises in these math worksheets are paced at increasing difficulty to help students grasp the topic better. By practicing these worksheets, students can identify the difference ..., Honors Geometry Parallel Lines cut by a Transversal Questions 1-6, use Figure 1. Assume ‖ and ‖ 1. What is the name for the angle pair 2 and 14. 2. What is the name for the angle pair 6 and 7 3. Name all angles congruent to 4 4. Name all angles supplementary to 6 5. If 16 = 50, then 14= ____ and 2 = _____, Parallel lines proving proofs studylib. Geometry worksheet parallel lines proving proofs pdf printableProving lines parallel worksheet / proving lines parallel ck 12 3 3 proving lines parallel worksheet answers …, 3.3 Proofs with Parallel Lines EXPLORE IT Work with a partner. Write the converse of each conditional statement. Determine whether the converse is true. Justify your conclusion. a. Corresponding Angles Theorem If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 4 2 3 6 8 7 5 b. Alternate ..., Unit 6: Analytic geometry. 0/1000 Mastery points. Distance and midpoints Dividing line segments Problem solving with distance on the coordinate plane. Parallel & perpendicular lines on the coordinate plane Equations of parallel & perpendicular lines., Level: grade 9. Language: English (en) ID: 984387. 08/05/2021. Country code: AE. Country: United Arab Emirates. School subject: math (1066928) Main content: Proving lines are parallel by parallel lines postulates (1371444) proving lines are parallel by parallel lines postulates., Worksheets are Proofs with perpendicular lines, Honors geometry chapter 3 proofs involving parallel and, Geometry beginning proofs packet 1, Parallel and perpendicular lines, Geometry proofs and postulates work, Geometry proof practice answers, Math work, Chapter 3 parallel and perpendicular lines. *Click on Open button to open and print to ..., Unit 6: Analytic geometry. 0/1000 Mastery points. Distance and midpoints Dividing line segments Problem solving with distance on the coordinate plane. Parallel & perpendicular lines on the coordinate plane Equations of parallel & perpendicular lines., SaaS small businesses are facing challenging macroeconomic conditions once again. Here are 5 tips for recession-proofing your SMB. SaaS small businesses are facing challenging macr..., This module deals with parallel, perpendicular and intersecting lines. A variety of pdf exercises and word problems will help improve the skills of students in grade 3 through grade 8 to identify and differentiate between parallel, perpendicular and intersecting lines. Some of them are absolutely free of cost! , 1.and have no points in common. and are parallel. 2.and have only one point in common. and intersect. 3.and have all points in common. and are the same line. These three possibilities can also be stated in the following postulate: Postulate 9.1Two distinct coplanar lines are either parallel or intersecting. CD., These math worksheets should be practiced regularly and are free to download in PDF formats. Parallel Lines Worksheet - 1. Download PDF. Parallel Lines Worksheet - 2. Download PDF. Parallel Lines Worksheet - 3. Download PDF. Parallel Lines Worksheet - 4. Download PDF., Unit test. Level up on all the skills in this unit and collect up to 1,900 Mastery points! In this topic, we'll learn about special angles, such as angles between intersecting lines and triangle angles. Next, we'll learn about the Pythagorean theorem. Finally, we'll find volume of curved 3D shapes like spheres, cones, and cylinders., Section 3.2 Parallel Lines and Transversals 133 Using Properties of Parallel Lines Find the value of x. a b 4 115° (x + 5)°SOLUTION By the Vertical Angles Congruence Theorem (Theorem 2.6), m∠4 = 115°.Lines a and b are parallel, so you can use the theorems about parallel lines. m∠4 + (x + 5)° = 180° Consecutive Interior Angles Theorem 115° + (x + …