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Notes 5A Congruence and Triangles.notebook October 31, 2011 Bell work Graph the equation 3x + 2y = 2 Notes 5A: Congruence and Triangles Goal: Identify congruent figures and corresponding parts. Vocabulary: When two geometric figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent 1. Given that CAT DOG, name three pairs of congruent sides. C D A T 2. Given ABC O G XYZ, name three pairs of congruent angles Y B A X C Z 1 Notes 5A Congruence and Triangles.notebook In the diagram, A ABC October 31, 2011 DEF, Complete the statement. D 80 8cm C 35 B F 1. <C ______ 2. BC _______ E 5. AC=______ 6. FDE ______ 3. m<A= ______ 4. m<F= _______ There are 5 ways to prove triangles are congruent. 1. Postulate 19: side-side-side (sss) if three sides of one trianlge are congruent to three sides of a second triangle, then they are congruent. Draw an example: 2. Postulate 20: side-angle-side (sas) If two sides and the included angle (the angle must be between the ~ = sides) of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. Draw an example: 2 Notes 5A Congruence and Triangles.notebook October 31, 2011 3. Postulate 21: angle-side-angle (asa) If two angles and the included side (side must be between the two ~ = angles) of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Draw an example: 4. Theorem 4.5: angle-angle-side (aas) If two angles and a non-included side (the side is not between the 2 ~ = angles) of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. Draw an example: 5. Hypotenuse-leg (HL) congruence theorem If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second triangle, then the two triangles are congruent. Draw an example: 3 Notes 5A Congruence and Triangles.notebook October 31, 2011 example: proving triangles are congruent 1. 2. 3. ( ( 5. 4. Complete the statement. ~ = ABC, then XY ~ = _____ 1. If XYZ 2. If BAT ~ = DOG, then <T ~ = _____ 3. If SAP ~ = MET, then PS ~ = _____ 4. If GHI ~ = PQR, then IH ~ = _____ 5. If RUN ~ = BAT, then 6. If PMN ~ = CRS, then <M ~ = _____ NRU ~ = _____ 4 Notes 5A Congruence and Triangles.notebook October 31, 2011 Identify any figures that can be proved congruent. Explain your reasoning. For those that can be proved congruent, write a congruence statement. ) E P ) G N 2. F T ) ) ) ) Q ) D ) 1. M R NOT Possible 3. X ( Y W ( Z Find the value of x and y. B ABC A DEF F C 22 ~ = 3x 9 (5y-3) E D 5 Notes 5A Congruence and Triangles.notebook October 31, 2011 Assignment Worksheet 5A 6