LESSON AAS Triangle Congruence 6-2 Practice And Problem .

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Name Date ClassLESSON6-2AAS Triangle CongruencePractice and Problem Solving: A/B1. Students in Mrs. Marquez’s class are watching a film on the uses ofgeometry in architecture. The film projector casts the image on a flatscreen as shown in the figure. The dotted line is the bisector of AC.Can you use the AAS Theorem to prove thatABD CBD ? Explain why or why not. Write whether the AAS Congruence Theorem, the ASA CongruenceTheorem, or neither can be used to prove the pair of triangles congruent.2.3.4.5.Write a paragraph proof.6. Given: PQU TSU QUR and SUR are right angles.Prove: RUQ RUS Original content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.111

Name Date ClassLESSON6-3HL Triangle CongruencePractice and Problem Solving: A/BFor Problems 1–3, use the HL Congruence Theorem to determine ifthe given triangles are congruent. For Problems 2 and 3, make surethe triangles are right triangles. Explain your answers.PQR and STU1. 2. A( 2, 2); B(4, 4); C( 2, 4); D(1, 1) ACD and BCD3. A(0, 2); B( 4, 0); C(0, 3); D( 2, 1)ACD and BCD 4. Complete the proof.Given: isosceles triangle ΔPQS with PQ PSand PR QSProve: PQR PSRStatementsReasons1.1. Given2. PRQ and PRS are rightangles.2.3.3. Definition of right triangle4.4.5.5.Original content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.116

Name Date ClassLESSON6-2AAS Triangle CongruencePractice and Problem Solving: ModifiedFill in the missing words for the AAS Congruence Theorem. Thefirst one is done for you.?If two angles and aside of one triangle are1.nonincluded?congruent to theangles and nonincluded side2.?of another triangle, then the triangles are .3.List the three congruence statements and the justifications neededto prove the triangles are congruent using the AAS CongruenceTheorem. The first one is done for you.Given: M is the midpoint of AB.Prove: AMC BMD A B, given4.5.6.Determine if you can use the AAS Theorem to prove the trianglescongruent. Explain. The first one is done for you.7.PQR and USP8.ABC and DEF 9. Yes; P U , PR SU , and R Taregiven on the figure. GKI and JKI10. UWV and XVWOriginal content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.113

Name Date ClassLESSON6-2AAS Triangle CongruenceReteachGiven two triangles, it can be shown that they are congruentby showing that two angles and a non-included side arecongruent.Since A D, B E, and AC DF ,ABC DEF . This is called the AAS Congruence Theorem.For each pair of triangles, state “yes” if they are congruent by the AAStheorem. Otherwise state “no” and explain why they are not congruent byAAS.1.2.Given the indicated information, what information is needed to show thatthe two triangles are congruent using the AAS theorem? There may bemore than one correct answer.4. A E3. B EOriginal content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.77

Name Date ClassLESSON6-3HL Triangle CongruenceReteachTwo right triangles are congruent if theirhypotenuses and one pair of legs arecongruent.If BC EF and AC DF , then ABC DEF.Consider triangles ABD and CBD in the figure.1. Which angle is the right angle in triangle ADB?Why?2. Name the corresponding legs from eachtriangle that are congruent.3. If AB 4 and BC 4, are the trianglescongruent? Why or why not?In the figure, ACDE is a square and CD 5.4. What is the length of AC ?5. What is the length of AE ?6. Can it be said thatnot? ABC AFE? Why or whyOriginal content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.78

Name Date ClassLESSON6-3HL Triangle CongruencePractice and Problem Solving: ModifiedFill in the missing words to complete the HL Theorem. The first one isdone for you.hypotenuse and a leg of one right triangle are congruentIf the 1.to the hypotenuse and a 2. of another 3.triangle, then the triangles are 4. .For each pair of triangles in Problems 5–8, identify the congruenthypotenuses and legs, if given. If the triangles are definitelycongruent by HL, write “yes.” If you cannot tell, write “?.” The firstone is done for you.5.6.ABC and DEFABD and DCA not givenHypotenuses:Hypotenuses:BC EFLegs:Legs:?Congruent:Congruent:7. ABC and DEC8. AMC and BMCM is the midpoint of gruent:Original content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.118

For each pair of triangles, state “yes” if they are congruent by the AAS theorem. Otherwise state “no” and explain why they are not congruent by AAS. 1. _ 2. _ Given the indicated information, what information is needed to show that the two triangles are

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