Day 6: Triangle Congruence, Correspondence and Styles of Proof HOMEWORK

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1 Day 6: Triangle Congruence, Correspondence and Styles of Proof HOMEWORK 1. If AB DE and ABC DEF as shown in the diagram, what additional information would make the triangles congruent using only SAS SAS (1) AC DF (2) BC EF (3) ACB DFE (4) BAC EDF 2. If AB DE and ABC DEF as shown in the diagram, what additional information would make the triangles congruent using only ASA ASA (1) AC DF (2) BC EF (3) ACB DFE (4) BAC EDF JKL DEF 3. In the diagram below of and, a sequence of rigid motions maps JK onto. Determine and state whether KL EF. Explain why. K E onto DE, J onto D and For #4-6: Given the following information, mark the diagram and then state your conclusions. AC 4. Given: bisects ÐBCD 1. bisects 1.Given AC ÐBCD Given: E is the midpoint of AB 1. E is the midpoint of 1.Given AB Given: CD ^ AB 1. CD ^ AB 1.Given

2 Day 7: Congruence Criteria for Triangles- SSS HOMEWORK 1. In the diagram below of and, and onto DF. EF DEF, a sequence of rigid motions maps AB onto DE, BC onto Determine and state whether A D. Explain why. 2. If BA CD SSS SSS and as shown in the diagram, what additional information would make ABD DCA using only (1) BDA CAD (3) ACD DBA (2) AE DE (4) AC DB SEPARATE TRIANGLES (and label reflexive property) In the diagram below, AD CB and AB CD, prove that ABD CDB. B A D C 2

3 Day 8: Congruence Criteria for Triangles- SAS HOMEWORK ABE and CBD 1. Given shown in the diagram below with DB BE. Which statement is needed to prove ABE CBD using only SAS SAS? SEPARATE TRIANGLES(look for reflexives) (1) CDB AEB (3) AB BC (2) AFD EFC (4) AE CD 2. In ABC and YBX below, BC BX, BY BA, and XY CA. Which method proves AYB ZYX? (1) SSS SSS (3) AAS AAS (2) SAS SAS (4) ASA ASA a) What rigid motion maps ABC onto YBX In the diagram of JKL and NML below, KM and JN bisect each other. Prove that JKL NML b) Precisely describe the rigid motion(s) that would map NML onto JKL 3

4 Day 9: Congruence Criteria for Triangles- ASA HOMEWORK 1. Given XA XB. Which additional statement is needed to prove AXZ BXY by ASA ASA? Separate Triangles 1) BYX AZX 3) AC BC 2) ZAX YBX 4) BY AZ 2. In the diagram below of ABC and DEF, a sequence of rigid motions maps AC onto DE. AB onto DF, A onto D and Determine and state whether C F. Explain why. 3. If XYZ JKL. Which of the following statements is not necessarily true? (1) XYZ JKL (3) XZY LKJ (2) YZX KLJ (4) XY JK 4. In the diagram of ABD and CBD below, BD AC, and D is the midpoint of AC B a) Prove that ADB CDB A D C b) Precisely describe the rigid motion that maps ABD to CBD 4

5 Day 11: Congruence Criteria for Triangles- AAS HOMEWORK 1. In the diagram below of and, a sequence of rigid motions maps onto, onto, and AB onto XY. Which method proves these triangles congruent? 1) SAS SAS 2) AAS AAS 3) ASA ASA 4) These triangles are NOT congruent 2. In the diagram shown, AB DC and E is the midpoint of. Determine and state whether. Explain your answer In the diagram show AC bisects ÐDAB, and a) Prove that ABC ADC and DC b) Precisely describe the rigid motion that maps ABC to ADC 5

6 Day 12: Congruence Criteria for Triangles- HL HOMEWORK 1. In the diagram shown it is given that CA ^ AB and DB ^ AB and M is the midpoint of AB. To prove AMC BMD by hypotenuse-leg only, which additional information would you need? 1) AC BD 2) DM 3) AM BM 4) ACM BDM 2. Which statement is sufficient evidence that is congruent to? 1) There is a sequence of rigid motions that maps onto, and onto. 2),, 3), and 4)There is a sequence of rigid motions that maps onto, onto, and onto. 3. In the diagram of and below,,, and. a) Prove that. b) Describe a sequence of rigid motions that will map onto. 6

7 Day 13: Congruence Criteria for Triangles- Addition/Subtraction HOMEWORK 1. In the diagram of below,. Which reasons can be used to prove? 1) reflexive property and addition postulate 2) reflexive property and subtraction postulate 3) transitive property and addition postulate 4) transitive property and subtraction postulate 2. As shown in the diagram below AB AE SAS SAS only? 1 2 1) 2) BC ED 3) ADB ACE 4) EC BD A B 1 2 E. Which piece of information is needed to prove ABD AEC by C D Separate Triangles 3. In the diagram shown BC EF, and AF DC a) Fill in the missing reasons to prove that 1. BC EF 1. Given 2. BCA EFD Given 4. AF DC 4. Given 5. FC FC AC DF ABC DEF b) Precisely describe a sequence of rigid motions that will map ABC onto DEF 7

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