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Transcript

Geometry Section 5.2 Congruent Polygons What you will learn: 1. Identify and use corresponding parts 2. Use the third angle theorem In simple terms, two polygons are congruent if they have exactly the same size and shape. More formally, two polygons are congruent iff a rigid motion or composition of rigid motions maps one onto the other. * A rigid motion maps each part of the preimage to a corresponding part in the image. *Because rigid motions preserve angle measure and side lengths, corrsponding angles and sides are congruent GE EN NO GO G E O N YS ST AT AY Y S A T congruence statement YATS DO N ACT x28 x6 6 2 y 84 2 y 78 y 39 Theorem 5.4 Third Angles Theorem If two angles of one triangle are congruent to two angles of second triangle then, the third angles are also congruent. To prove two triangles are congruent using the definition of congruent polygons, one must show that all 6 pairs of corresponding parts are congruent. AO ON VOA & VON are Rt Ang. VOA VON AVO NVO AVO NVO AVO NVO Given Definition of midpoint Definition of perpendicular Right Angles Cong. Theorem Definition of angle bisector All Corr. Parts Cong. AO ON VOA & VON are Rt Ang. VOA VON AVO NVO AVO NVO VO VO AVO NVO Given Definition of midpoint Definition of perpendicular Right Angles Cong. Theorem Definition of angle bisector Third Angle Theorem Reflexive Property All Corr. Parts Cong. In subsequent sections, you will see that it is possible to prove that some triangles are congruent by using only three pairs of congruent parts! Theorem 5.3 Properties of Triangle Congruence HW: p243 / 4-10, 12-14