Triangle Similarity: AA, SSS, SAS Quiz

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1 Name: lass: ate: I: Triangle Similarity:, SSS, SS Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Explain why the triangles are similar and write a similarity statement. a. E and E by the orresponding ngles Postulate. b. E and E by the lternate Interior ngles Theorem. c. E and E by the lternate Interior ngles Theorem. E by Similarity. d. E and E by the orresponding ngles Postulate. E by Similarity. 2. Verify that PQR SQT. a. Q Q by the Reflexive Property of ongruence. QS QP = QT QR = 3 5 PQR SQT by SS Similarity. b. P QST and R QTS by the orresponding ngles Postulate. PQR SQT by Similarity. c. P QTS and R QST by the lternate Interior ngles Theorem. PQR SQT by Similarity. d. Q Q by the Reflexive Property of ongruence. PS QP = QT QR = 2 5 PQR SQT by SS Similarity. 1

2 Name: I: 3. Explain why E and then find. a. Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. b. Ä E by the onverse of the lternate Interior ngles Theorem. E by the lternate Interior ngles Theorem. orresponding sides are proportional, so = 14. c. by the Reflexive Property of ongruence. orresponding sides are proportional, so = 14. d. E, E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. 2

3 I: Triangle Similarity:, SSS, SS Quiz nswer Section MULTIPLE HOIE 1. NS: Since Ä E, E, and E by the orresponding ngles Postulate. Therefore orrect! re angles, E and angles, E pairs of alternate interior angles? re angles, E and angles, E pairs of alternate interior angles? List the corresponding vertices in the same order when writing a similarity statement. PTS: 1 IF: verage REF: 1b82c df-9c7d f0d2ea OJ: Using the Similarity Postulate NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles correspondence similarity OK: OK 2 2. NS: Q Q by the Reflexive Property of ongruence. QS QP = 6 10 = 3 5, QT QR = 9 15 = 3 5 Therefore E by SS Similarity. orrect! Is it given that segment PR is parallel to ST? Is it given that segment PR is parallel to ST? re the angle pairs in this choice alternate interior angles? Is segment PS a side of one of the triangles? re the ratios equal? PTS: 1 IF: verage REF: 1b82ea df-9c7d f0d2ea OJ: Verifying Triangle Similarity NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 NY.NYLES.MTH.05.GEO.G.G.45 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles SS similarity OK: OK 2 1

4 I: 3. NS: Step 1 Prove triangles are similar. s shown E, so Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. Therefore Step 2 Find. E = E orresponding sides are proportional = 28 Substitute 32 for E, 48 for, and 28 for E. 32() = ross Products Property 32() = 1344 Simplify. = 42 ivide both sides by 32. orrect! re angles and E and angles and E pairs of alternate interior angles? an equal 14 if E equals 28? You found the value of E, not. It is given that angles and E are congruent. You are also missing one step before concluding that angles and E are congruent. PTS: 1 IF: verage REF: 1b85256e df-9c7d f0d2ea OJ: Finding Lengths in Similar Triangles NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles side length similarity OK: OK 2 2

5 Name: lass: ate: I: Triangle Similarity:, SSS, SS Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Explain why the triangles are similar and write a similarity statement. a. E and E by the orresponding ngles Postulate. E by Similarity. b. E and E by the orresponding ngles Postulate. c. E and E by the lternate Interior ngles Theorem. E by Similarity. d. E and E by the lternate Interior ngles Theorem. 2. Verify that PQR SQT. a. P QTS and R QST by the lternate Interior ngles Theorem. PQR SQT by Similarity. b. Q Q by the Reflexive Property of ongruence. QS QP = QT QR = 3 5 PQR SQT by SS Similarity. c. P QST and R QTS by the orresponding ngles Postulate. PQR SQT by Similarity. d. Q Q by the Reflexive Property of ongruence. PS QP = QT QR = 2 5 PQR SQT by SS Similarity. 1

6 Name: I: 3. Explain why E and then find. a. Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. b. by the Reflexive Property of ongruence. orresponding sides are proportional, so = 14. c. Ä E by the onverse of the lternate Interior ngles Theorem. E by the lternate Interior ngles Theorem. orresponding sides are proportional, so = 14. d. E, E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. 2

7 I: Triangle Similarity:, SSS, SS Quiz nswer Section MULTIPLE HOIE 1. NS: Since Ä E, E, and E by the orresponding ngles Postulate. Therefore List the corresponding vertices in the same order when writing a similarity statement. orrect! re angles, E and angles, E pairs of alternate interior angles? re angles, E and angles, E pairs of alternate interior angles? PTS: 1 IF: verage REF: 1b82c df-9c7d f0d2ea OJ: Using the Similarity Postulate NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles correspondence similarity OK: OK 2 2. NS: Q Q by the Reflexive Property of ongruence. QS QP = 6 10 = 3 5, QT QR = 9 15 = 3 5 Therefore E by SS Similarity. Is it given that segment PR is parallel to ST? re the angle pairs in this choice alternate interior angles? orrect! Is it given that segment PR is parallel to ST? Is segment PS a side of one of the triangles? re the ratios equal? PTS: 1 IF: verage REF: 1b82ea df-9c7d f0d2ea OJ: Verifying Triangle Similarity NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 NY.NYLES.MTH.05.GEO.G.G.45 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles SS similarity OK: OK 2 1

8 I: 3. NS: Step 1 Prove triangles are similar. s shown E, so Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. Therefore Step 2 Find. E = E orresponding sides are proportional = 28 Substitute 32 for E, 48 for, and 28 for E. 32() = ross Products Property 32() = 1344 Simplify. = 42 ivide both sides by 32. orrect! You found the value of E, not. re angles and E and angles and E pairs of alternate interior angles? an equal 14 if E equals 28? It is given that angles and E are congruent. You are also missing one step before concluding that angles and E are congruent. PTS: 1 IF: verage REF: 1b85256e df-9c7d f0d2ea OJ: Finding Lengths in Similar Triangles NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles side length similarity OK: OK 2 2

9 Name: lass: ate: I: Triangle Similarity:, SSS, SS Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Explain why the triangles are similar and write a similarity statement. a. E and E by the lternate Interior ngles Theorem. b. E and E by the lternate Interior ngles Theorem. E by Similarity. c. E and E by the orresponding ngles Postulate. E by Similarity. d. E and E by the orresponding ngles Postulate. 2. Verify that PQR SQT. a. Q Q by the Reflexive Property of ongruence. PS QP = QT QR = 2 5 PQR SQT by SS Similarity. b. Q Q by the Reflexive Property of ongruence. QS QP = QT QR = 3 5 PQR SQT by SS Similarity. c. P QTS and R QST by the lternate Interior ngles Theorem. PQR SQT by Similarity. d. P QST and R QTS by the orresponding ngles Postulate. PQR SQT by Similarity. 1

10 Name: I: 3. Explain why E and then find. a. Ä E by the onverse of the lternate Interior ngles Theorem. E by the lternate Interior ngles Theorem. orresponding sides are proportional, so = 14. b. E, E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. c. Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. orresponding sides are proportional, so = 42. d. by the Reflexive Property of ongruence. orresponding sides are proportional, so = 14. 2

11 I: Triangle Similarity:, SSS, SS Quiz nswer Section MULTIPLE HOIE 1. NS: Since Ä E, E, and E by the orresponding ngles Postulate. Therefore re angles, E and angles, E pairs of alternate interior angles? re angles, E and angles, E pairs of alternate interior angles? List the corresponding vertices in the same order when writing a similarity statement. orrect! PTS: 1 IF: verage REF: 1b82c df-9c7d f0d2ea OJ: Using the Similarity Postulate NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles correspondence similarity OK: OK 2 2. NS: Q Q by the Reflexive Property of ongruence. QS QP = 6 10 = 3 5, QT QR = 9 15 = 3 5 Therefore E by SS Similarity. Is segment PS a side of one of the triangles? re the ratios equal? orrect! Is it given that segment PR is parallel to ST? re the angle pairs in this choice alternate interior angles? Is it given that segment PR is parallel to ST? PTS: 1 IF: verage REF: 1b82ea df-9c7d f0d2ea OJ: Verifying Triangle Similarity NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 NY.NYLES.MTH.05.GEO.G.G.45 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles SS similarity OK: OK 2 1

12 I: 3. NS: Step 1 Prove triangles are similar. s shown E, so Ä E by the onverse of the orresponding ngles Postulate. E by the orresponding ngles Postulate. Therefore Step 2 Find. E = E orresponding sides are proportional = 28 Substitute 32 for E, 48 for, and 28 for E. 32() = ross Products Property 32() = 1344 Simplify. = 42 ivide both sides by 32. re angles and E and angles and E pairs of alternate interior angles? an equal 14 if E equals 28? It is given that angles and E are congruent. You are also missing one step before concluding that angles and E are congruent. orrect! You found the value of E, not. PTS: 1 IF: verage REF: 1b85256e df-9c7d f0d2ea OJ: Finding Lengths in Similar Triangles NT: NT.SS.MTH G.SRT.5 ST: NY.NYLES.MTH.05.GEO.G.G.44 LO: MTH TOP: 7-3 Triangle Similarity:, SSS, and SS KEY: similar triangles side length similarity OK: OK 2 2

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