4.3: Analyzing Triangle Congruence Expectations: G2.3.1: Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria and that right triangles are congruent using the hypotenuse-leg criterion. G2.3.2:Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence AAA Conjecture a. Draw a 30°, 60°, 90 right triangle. b. Compare your triangle to a neighbor’s. c. What can be said about the triangles? 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence AAA Conjecture AAA is not sufficient to conclude triangles are congruent. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence SSA Conjecture a. Draw a triangle with 2 sides that are 8cm and 6 cm, with a non-included angle of 40. b. Compare your triangle to a neighbor’s. c. What can be said about the triangles? 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence SSA Conjecture SSA is not sufficient to prove triangles are congruent. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence SsA A very special case of SSA is valid for proving triangles congruent. It is referred to as SsA. In SsA, the angles given must be opposite the longer of the 2 sides. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence SsA E B F C D A Given the above information, ΔABC  ΔDEF. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence SsA In two triangles, if two sides of the first are congruent to two sides of the second and the angle opposite the longer of the two sides of the first is congruent to the corresponding angle of the second triangle, then the triangles are congruent. 4/17/2017 4.3: Analyzing Triangle Congruence

Are the triangles congruent? Justify your answer. Z C 10 in 10 in 50º 60º 50º 60º A B Y X 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence Non-Included Sides C AC is a nonincluded side for A and B BC is a nonincluded side for A and B B A 4/17/2017 4.3: Analyzing Triangle Congruence

AAS Congruence Theorem If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of the second triangle, then the triangles are congruent. 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence HL Congruence Theorem In 2 right triangles, if the hypotenuse and a leg of the first are congruent to the hypotenuse and a leg of the second, then the triangles are congruent. 4/17/2017 4.3: Analyzing Triangle Congruence

Prove the HL Congruence Theorem F C A B D E Given: AC = DF and BC = EF Prove: ABCDEF 4/17/2017 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle Congruence Assignment pages 231-234, # 10-18 (evens), 20-29 (all), 30, 32, 34, 35, 37, 42, 43 4/17/2017 4.3: Analyzing Triangle Congruence