Unit 4 Take Home Proofs - Teachers.Henrico Webserver

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Name: Period: Date: ID: ACongruent Triangles Quiz - HonorsMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1. (1 point) Given: ΔABE ΔDBC. (The two TRIANGLES arecongruent.) Why is AEB DCB ?A) ASAB) AASC) CPCTCD) SASE) HLF) SSSG) SSA2. (1 point) In the diagram below, LN ON . What additional information isneeded to prove that ΔMNL is congruent to ΔPNO by ASA?A) MN PNB) L OC) M PD) LM OPShort Answer3. (2 points) What is wrong with the following diagram? (Answer withcomplete sentences, using appropriate geometric language.)1

Name:4. (1 point) Given ABC ID: AXYZ, AB 15 , AC 30 , YZ 25 , andXY 5x 20 , find x.5. (3 points) The two triangles are congruent as suggested by their appearance. Thediagrams are not to scale. Find the values of the variables b, d, and e.b d e Use the given information to label the diagram and decide whether the trianglesare congruent. Then name the congruence postulate or theorem you used. Namethe congruent triangles, if any. If they are not congruent (or can’t be shown tobe congruent), write, “cannot be determined.” (Don’t fill in the blanks!)6. (3 points) Given A E and AC EC.ΔABC Δ by (postulate or theorem)7. (3 points) Given: FEG HEG and FE HEΔEFG Δ by (postulate or theorem)2

Name:ID: A8. (3 points) Given: LB MB and m ALB 90 and m AMB 90 .ΔALB Δ by (postulate or theorem)9. (2 points) Given: M and B are right angles, and MZ Ä BQΔMZQ Δ by (postulate or theorem)10. (3 points) Given: HFS IFS and IS HSΔIFS Δ by (postulate or theorem)11. (3 points) Given: WT Ä AH and T HΔWHA Δ by (postulate or theorem)3

Name:ID: A12. (3 points) Given: B is the midpoint of DQΔZDB Δ by (postulate or theorem)13. (3 points) Given: BAD BCD and BD bisects angle ABC.ΔBDA Δ by (postulate or theorem)14. (3 points) Given: RT QT and AT ST TQS by (postulate or theorem)15. (3 points) Given: CE DF and CF DE CFE by (postulate or theorem)4

Name:ID: AEssay16. (6 points) Given: B is the midpoint of AD, and B is the midpoint of EC.Prove: E C17. (6 points) Given: AE Ä DC and AE DCProve: AB DB18. (6 points) Given: RT QT and AT STProve: RA QS19. (6 points) Given: QAR and RSQ are right angles, and RS QAProve: RA QS5

Name:ID: A 20. (1 point) CB bisects ACD and AB bisects CAD. The measure of CBA is 100 degrees. Find x m E. (Hint: Let a m CABand c m ACB.)6

ID: ACongruent Triangles Quiz - HonorsAnswer SectionMULTIPLE CHOICE1. ANS: C2. ANS: BSTA: G.5STA: G.5SHORT ANSWER3. ANS:The triangles are congruent by ASA, but AE DC. Both are not possible.4. ANS:7STA: G.55. ANS:606.7.8.9.10.11.STA: VA G.5a VA G.5bANS:ΔABC ΔEDC by ASAANS:EHG, SASANS:ΔALB ΔAMB by HL.ANS:ΔMZQ ΔBQZ by AASANS:cannot be determined (SSA)ANS:WTA by AAS1

ID: A12. ANS:ΔZDB ΔLQB by SSS.13. ANS:AAS14. ANS:ΔTQS ΔTRA by SAS15. ANS:ΔCFE ΔDEF by SSSESSAY16. ANS:reasons:given(S)defn midpoint(A) vertical angles theoremgiven(S)defn midpointcongruent triangles by SAS.CPCTC17. ANS:given(A)alt. int angles thm(S) given(A)alt. int angles thmcongruent triangles by ASA (or use vertical angles theorem and AAS)CPCTC2

ID: A18. ANS:given(S)given(A) T T (reflexive property of )(S)givencongruent triangles by SASCPCTC19. ANS: QAR and RSQ are right angles (given)ΔQAR and ΔRSQ are right triangles. (defn right triangle)(H) RQ QR (reflexive property of )(L) RS QA (given)congruent triangles by HLCPCTC20. ANS:Let a m CAB m BAELet c m ACB m BCDa c 100 180 (triangle sum theorem on triangle ABC)a c 80 (subtraction property)2a 2c x 180(triangle sum theorem on triangle AEC)2(a c) x 180 (distributive property)2(80) x 180 (substitution property)x 20 (subtraction property)3

Identify the choice that best completes the statement or answers the question. 1. (1 point) Given: ΔABE DBC. (The two TRIANGLES are congruent.) Why is AEB DCB? A) ASA C) CPCTC E) HL G) SSA B) AAS D) SAS F) SSS 2. (1 point) In the diagram below, LN ON. What additional inf