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Opener Sect. 4.2 Congruence and Triangles Goal 1 Identifying Congruent Figures Goal 2 Proving Triangles are Congruent Identifying Congruent Figures Two geometric figures are congruent if they are the same size and shape • Their corresponding angles and sides are equal. Example: The pentagons are congruent. Identifying Congruent Figures Congruent Triangles Figures that have the same size and shape Example: The triangles are congruent. Identifying Congruent Figures If two figures are congruent, then their corresponding parts are congruent. Look at the corresponding parts of ABC and DFE. A B ABC C D DFE F E A triangle has three sides and three angles. If two triangles are congruent, then the sides and angles that match are called corresponding parts. A corresponds to D B corresponds to F C corresponds to E side AB corresponds to side DF side BC corresponds to side FE side CA corresponds to side ED. Identifying Congruent Figures Write a congruence statement for the two triangles. Then identify all pairs of congruent A corresponding parts. B E 98° 98° C D F Identify all the pairs of congruent parts if DWV PJS Regardless of how the diagram appears you can determine all the congruent corresponding parts based on the congruence statement provided. V D P W J S Identifying Congruent Figures Corresponding Parts of Congruent Triangles are Congruent CPCTC Identifying Congruent Figures In the diagram, ABCD KJHL 1) Find the value of x 2) Find the value of y J A 9 cm B 91° (5y - 12)° H (4x - 3) cm D 86° 113° 6 cm C K L Identifying Congruent Figures Theorem 4.3 Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. If A D and B F, Then C E Identifying Congruent Figures Find the value of x. B 87° A 22° C F (4X + 15)° E D Proving Triangles are Congruent Given: MN QP; MN || PQ; M N O is midpoint of MQ and PN Prove: MNO QPO 1. MN QP 1. Given 2. MN || QP 2. Given 3. OMN OQP 3. Alt Interior Angles 4. ONM OPQ 4. Alt Interior Angles 5. MON POQ 5. Vertical Angles 6. O is the midpoint of MQ and PN 6. Given 7. MO OQ, PO ON 7. Def of a midpoint 8. ∆MNO ∆QPO 8. CPCTC O P Q Homework 4.2 Exs. 10 – 28 even, 46-56 even