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Geometry 5.2 Notes: Congruent Polygons and Corresponding Parts Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Examples: 1. Find πβ π΅π·πΆ. 2. Find the values of x and y. From Chapter 4: Two figures are congruent if and only if a rigid motion or a composition of rigid motions maps each part of a figure onto the other. ο A rigid motion maps each part of a figure to a corresponding part of its image. ο Because rigid motions preserve length and angle measure, corresponding parts of congruent figures are congruent. This means that corresponding _____________ and corresponding _________________ are ________. Using Rigid Motions to prove two figures are congruent Now that we know the two triangles above are congruent, we can write a _________________________________. Example: 3. Write a congruence statement for the triangles. Identify all parts of congruent, corresponding parts. 4. In the diagram, π·πΈπΉπΊ β ππππ . a. Find the value of x. b. Find the value of y. Showing That Figures are Congruent Example: 5. You divide the wall into orange (left) and blue (right) sections along Μ Μ Μ π½πΎ . Will the sections of the wall be the same size and shape? Explain. Properties of Triangle Congruence Reflexive: Symmetric: Transitive: