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Similar and Congruent Triangles MPM2D Ms. Kueh Two triangles may be congruent, similar, or neither. The order of the letters naming the vertices of congruent or similar triangles indicates the order in which the vertices, sides, and angles of one triangle correspond to the vertices, sides, and angles of the other. Congruent Similar Definition: Definition: _____________________ are identical in every way. They have exactly the same shape and size. The expression ______________________ have the same shape, but are different sizes. One triangle is an larger or smaller than the other. The expression means that ΔABC is _____________ to ΔXYZ If ΔABC ΔXYZ, then means that ΔABC is _____________ to ΔXYZ If ΔABC ~ ΔXYZ, then Corresponding sides are equal Corresponding sides are proportional Corresponding angles are equal. and Corresponding angles are equal Example 1 Name the similar triangles. Write the letters so that equal angles appear in corresponding order. Example 2 Determine the unknown measures a) b) Example 3 Find the value of each indicated quantity. Example 4 Solve for an Unknown Side To determine the width of a river, Naomi finds a willow tree and a maple tree that are directly across from each other on opposite shores. Using a third tree on the shoreline, Naomi plants two stakes, A and B, and measures the distances shown. Find the width of the river. Homework: pg. 462 #7 pg. 538 #1-7