AAS Triangle Congruence

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Erick Watson
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1 Name Date Class 6-2 AAS Triangle Congruence Practice and Problem Solving: A/B 1. Students in Mrs. Marquez s class are watching a film on the uses of geometry in architecture. The film projector casts the image on a flat screen as shown in the figure. The dotted line is the bisector of AC. Can you use the AAS Theorem to prove that ABD CBD? Explain why or why not. Write whether the AAS Congruence Theorem, the ASA Congruence Theorem, or neither can be used to prove the pair of triangles congruent Write a paragraph proof. 6. Given: PQU TSU QUR and SUR are right angles. Prove: RUQ RUS 111

2 Name Date Class 6-3 HL Triangle Congruence Practice and Problem Solving: A/B For Problems 1 3, use the HL Congruence Theorem to determine if the given triangles are congruent. For Problems 2 and 3, make sure the triangles are right triangles. Explain your answers. 1. PQR and STU _ 2. A( 2, 2); B(4, 4); C( 2, 4); D(1, 1) ACD and BCD _ 3. 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 PS and PR QS Prove: PQR PSR Statements Reasons Given 2. PRQ and PRS are right angles Definition of right triangle

3 Name Date Class 6-2 AAS Triangle Congruence Practice and Problem Solving: Modified Fill in the missing words for the AAS Congruence Theorem. The first one is done for you. If two angles and a? side of one triangle are 1. nonincluded congruent to the? angles and nonincluded side of another triangle, then the triangles are.? List the three congruence statements and the justifications needed to prove the triangles are congruent using the AAS Congruence Theorem. The first one is done for you. Given: M is the midpoint of AB. Prove: AMC BMD 4. A B, given Determine if you can use the AAS Theorem to prove the triangles congruent. Explain. The first one is done for you. 7. PQR and USP 8. ABC and DEF Yes; P U, PR SU, and R T are given on the figure. 9. GKI and JKI 10. UWV and XVW 113

4 Name Date Class 6-2 AAS Triangle Congruence Reteach Given two triangles, it can be shown that they are congruent by showing that two angles and a non-included side are congruent. 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 AAS theorem. Otherwise state no and explain why they are not congruent by AAS Given the indicated information, what information is needed to show that the two triangles are congruent using the AAS theorem? There may be more than one correct answer. 3. B E 4. A E 77

5 Name Date Class 6-3 HL Triangle Congruence Reteach Two right triangles are congruent if their hypotenuses and one pair of legs are congruent. 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 each triangle that are congruent. 3. If AB = 4 and BC = 4, are the triangles congruent? Why or why not? In the figure, ACDE is a square and CD = What is the length of AC? 5. What is the length of AE? Why or why 6. Can it be said that ABC AFE? not? 78

6 Name Date Class 6-3 HL Triangle Congruence Practice and Problem Solving: Modified Fill in the missing words to complete the HL Theorem. The first one is done for you. If the 1. hypotenuse and a leg of one right triangle are congruent 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 congruent hypotenuses and legs, if given. If the triangles are definitely congruent by HL, write yes. If you cannot tell, write?. The first one is done for you. 5. ABC and DEF 6. ABD and DCA not given BC EF Congruent:? Congruent: 7. ABC and DEC 8. AMC and BMC M is the midpoint of AB. Congruent: Congruent: 118

Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º.

Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º. Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º. No-Choice Theorem If two