4.2 Apply Congruence and
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- Hector Hardy
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1 4.2 pply ongruence and riangles oal p Identify congruent figures. Your Notes VOULRY ongruent figures orresponding parts o help you identify corresponding parts, turn n. xample 1 Identify congruent parts Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. he diagram indicates that n > n. orresponding angles >, >, > orresponding sides >, >, > xample 2 In the diagram, QR > WXYZ. a. ind the value of x. b. ind the value of y. Use properties of congruent figures R 6 in Z 658 (5x 1 5)8 W (y 2 x) in. Y X a. You know Q > W. b. You know QR > WX. m Q 5 QR x 5 y opyright olt Mcougal. ll rights reserved. Lesson 4.2 eometry Notetaking uide 93
2 4.2 pply ongruence and riangles oal p Identify congruent figures. Your Notes VOULRY ongruent figures In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. orresponding parts In congruent polygons, the corresponding parts are the corresponding sides and the corresponding angles. o help you identify corresponding parts, turn n. xample 1 Identify congruent parts Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. he diagram indicates that n > n. orresponding angles >, >, > orresponding sides >, >, > xample 2 In the diagram, QR > WXYZ. a. ind the value of x. b. ind the value of y. Use properties of congruent figures R 6 in Z 658 (5x 1 5)8 W (y 2 x) in. Y X a. You know Q > W. b. You know QR > WX. m Q 5 m W QR 5 WX (5x 1 5)8 6 5 y 2 x x 6 5 y x 18 5 y opyright olt Mcougal. ll rights reserved. Lesson 4.2 eometry Notetaking uide 93
3 heckpoint In xercises 1 and 2, use the diagram shown in which > UV. 1. Identify all pairs of congruent corresponding parts. U (2x 2 7) V 2. ind the value of x and find m. xample 3 how that figures are congruent Maps If you cut the rectangular map in half along PR, will the sections of the map be the same size and shape? xplain. P 1 rom the diagram, > because all right angles are congruent. lso, by the Lines Perpendicular to a ransversal heorem, PQ. hen 1 > and 2 > by the. o, all pairs of corresponding angles are. he diagram shows PQ > and QR >. y the, PR > RP. ll corresponding parts are, so npqr >., the two sections will be the same and R 94 Lesson 4.2 eometry Notetaking uide opyright olt Mcougal. ll rights reserved.
4 heckpoint In xercises 1 and 2, use the diagram shown in which > UV. 1. Identify all pairs of congruent corresponding parts. U (2x 2 7) V orresponding angles: >, >, > U, > V orresponding sides: >, > U, > UV, > V 2. ind the value of x and find m. x 5 55; m xample 3 how that figures are congruent Maps If you cut the rectangular map in half along PR, will the sections of the map be the same size and shape? xplain. P 1 rom the diagram, > Q because all right angles are congruent. lso, by the Lines Perpendicular to a ransversal heorem, PQ R. hen 1 > 4 and 2 > 3 by the lternate Interior ngles heorem. o, all pairs of corresponding angles are congruent. he diagram shows PQ > R and QR > P. y the Reflexive Property, PR > RP. ll corresponding parts are congruent, so npqr > nrp. Yes, the two sections will be the same size and shape R 94 Lesson 4.2 eometry Notetaking uide opyright olt Mcougal. ll rights reserved.
5 ORM 4.3: IR NL ORM If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also. xample 4 ind m V. Use the hird ngles heorem U > VUW by the. he diagram shows that U >, so by the hird ngles heorem, >. y the riangle um heorem, m 5 5. o, m 5 m V 5 by the definition of congruent angles U V W xample 5 Prove that triangles are congruent Write a proof. iven >, >, >, > Prove n > n Plan for Proof a. Use the Reflexive Property to show. b. Use the hird ngles heorem to show. Plan in ction tatements Reasons 1. >, > 1. a Reflexive Property of ongruence 3. >, 3. > b hird ngles heorem 5. n > n 5. opyright olt Mcougal. ll rights reserved. Lesson 4.2 eometry Notetaking uide 95
6 ORM 4.3: IR NL ORM If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. xample 4 ind m V. Use the hird ngles heorem U > VUW by the Vertical ngles heorem. he diagram shows that U > VWU, so by the hird ngles heorem, > V. y the riangle um heorem, m o, m 5 m V by the definition of congruent angles U V W xample 5 Prove that triangles are congruent Write a proof. iven >, >, >, > Prove n > n Plan for Proof a. Use the Reflexive Property to show >. b. Use the hird ngles heorem to show >. Plan in ction tatements Reasons 1. >, > 1. iven a. 2. > 2. Reflexive Property of ongruence 3. >, 3. iven > b. 4. > 4. hird ngles heorem 5. n > n 5. efinition of > ns opyright olt Mcougal. ll rights reserved. Lesson 4.2 eometry Notetaking uide 95
7 ORM 4.4: PROPRI O ONRUN RINL Reflexive Property of ongruent riangles or any triangle, n >. ymmetric Property of ongruent riangles If n > n, then. ransitive Property of ongruent riangles K If n > n and n > nkl, then. L heckpoint omplete the following exercises. 3. In the diagram at the right, is the midpoint of and. how that n > n. omework 4. In the diagram, what is the measure of? 5. y the definition of congruence, what additional information is needed to know that n > n in xercise 4? Lesson 4.2 eometry Notetaking uide opyright olt Mcougal. ll rights reserved.
8 ORM 4.4: PROPRI O ONRUN RINL Reflexive Property of ongruent riangles or any triangle, n > n. ymmetric Property of ongruent riangles If n > n, then n > n. ransitive Property of ongruent riangles K If n > n and n > nkl, then n > nkl. L heckpoint omplete the following exercises. 3. In the diagram at the right, is the midpoint of and. how that n > n. rom the diagram, >. Point is the midpoint of and, so > and > by the definition of midpoint. o all pairs of corresponding sides are congruent. he diagram shows i, so > and > by the lternate Interior ngles heorem. lso, > by the Vertical ngles heorem. ll corresponding parts are congruent, so n > n. omework 4. In the diagram, what is the measure of? y the definition of congruence, what additional information is needed to know that n > n in xercise 4? You must know that > and > to conclude that n > n. he remaining information can be inferred from the graph Lesson 4.2 eometry Notetaking uide opyright olt Mcougal. ll rights reserved.
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5.5 Start Thinking. 5.5 Warm Up. 5.5 Cumulative Review Warm Up. Use a ruler to construct JKL with JK = 1 in., KL = 0.5 in.,
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b. Move BC so that B is on the smaller circle and C is on the larger circle. Then draw ABC.
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Name: Review for inal 2016 Period: eometry 22 Note to student: This packet should be used as practice for the eometry 22 final exam. This should not be the only tool that you use to prepare yourself for
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Chapter 3: Congruent to Similar Figures (Triangles) Angles. Opposite Angles: Corresponding Angles: Alternate Interior Angles
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Solve each equation. EXAMPLE. Name &1 in two other ways. &AEC and &CEA are other names for &1. Quick Check
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escription Geometry S Review Geometry Review Question #1 If Δ and ΔXYZ are congruent, which of the following statements below is not true? ngle and angle Y are congruent. ngle and angle ZXY are congruent.