Name Date Class Period

Transcription

1 Name Date Class Period Activity B 4.6 Comparing Congruent Triangles MATERIALS metric ruler protractor QUESTION EXPLORE 1 If two triangles are congruent what do you know about the corresponding parts of the two triangles? Compare congruent triangles STEP 1 DRAW TWO TRIANGLES Using a ruler and protractor carefully redraw ΔABC and ΔGFE. STEP 2 Corresponding parts Complete the table with corresponding parts of the two triangles. ΔABC A B C AB AC BC ΔGFE STEP 3 Congruent parts List the parts of the two triangles that you know are congruent because of how you drew the triangles. STEP 4 Measure sides Measure the following sides to the nearest millimeter. AC = BC = GE= FE= 1 of 7

2 DRAW CONCLUSIONS Use your observations to complete these exercises Why are ΔABC and ΔGFE congruent? Are AC and GE congruent? What else can you say about AC and GE? Are BC and FE congruent? What else can you say about BC and FE? In Exercises 4 6 use ΔABC and ΔFGH Are ΔABC and ΔFGH congruent? Explain. Without measuring, are B and G congruent? Explain. Without measuring are AC and FH congruent? Explain. 7. Complete the following statement: If two triangles are congruent, then the corresponding parts of the two triangles are. 2 of 7

3 Answer Key B EXPLORE STEP 2 ΔABC A B C AB AC BC ΔGFE G F E GF GE FE STEP 3 A G; AB GF ; B F STEP 4 AC 10.9 cm; BC 6.4 cm; GE 10.9 cm; FE 6.4 cm DRAW CONCLUSIONS ASA Congruence Postulate Yes; they are corresponding parts. Yes; they are corresponding parts. yes; HL Congruence Theorem Yes; the triangles are congruent, so the corresponding parts of the triangles are congruent. Yes; the triangles are congruent, so the corresponding parts of the triangles are congruent. congruent 3 of 7

4 Teacher Notes ACTIVITY PREPARATION AND MATERIALS Students can work individually or in pairs. Each student or pair of students will need a metric ruler and a protractor ACTIVITY MANAGEMENT If students are working in pairs, have each student draw one of the triangles. Then the two students can answer the questions together using the two triangles. If students have a difficult time answering Exercises 5 and 6 you may want them to construct the triangles so that they can measure the angles. 4 of 7

5 Activity and Closure Questions Use ΔRST and ΔJKL to answer Exercises 1 4 as a class. 1. List the corresponding parts of ΔRST and ΔJKL. Answer: R corresponds to J; T corresponds to L; S corresponds to K; RT corresponds to JL ; SR corresponds to KJ ; ST corresponds to KL 2. Which parts are given and you know are congruent? Answer: SR KJ ; ST KL ; R J 3. Why are ΔRST and ΔJKL congruent? Answer: HL Congruence Theorem 4. Are S and K congruent? How do you know? Answer: Yes; corresponding parts of congruent triangles are congruent. Use ΔADB and ΔCDB to answer Exercises 5 8 as a class. 5. List the corresponding parts of ΔADB and ΔCDB. Answer: A corresponds to C; ABD corresponds to CBD; ADB corresponds to CDB; AD corresponds to CD ; BD corresponds to BD ; AB corresponds to CB 6. Which parts are given and you know are congruent? Answer: AB CB ; ABD CBD; BD BD ; ADB CDB 7. Are ΔADB and ΔCDB congruent? Explain why or why not. Answer: AAS Congruence Theorem, SAS Congruence Postulate, or HL Congruence Theorem 8. Why are AD and CD congruent? 5 of 7

6 Answer: Corresponding parts of congruent triangles are congruent. 6 of 7

7 Use ΔABC and ΔADC to answer Exercises 9 and 10 as a class. 9. List two triangles that are congruent and give a reason why they are congruent. Answer: ΔDAC ΔBCA; SSS Congruence Postulate 10. Why must D and B be congruent? Answer: Corresponding parts of congruent triangles are congruent. LESSON TRANSITION Students should start this activity familiar with the idea that corresponding parts of congruent triangles are congruent. The new idea in this lesson is that you can use given information to prove that triangles are congruent as a step toward proving that parts of the triangles with unknown measures are congruent. 7 of 7