Congruent Figures Congruent figures are two figures that have the same size and shape. IF two figures are congruent THEN they have the same size and shape. IF two figures have the same size and shape THEN they are congruent. Two figures have the same size and shape IFF they are congruent. Conditional: Converse: Biconditional:

Congruent Triangles - CPCTC CPCTC: Corresponding Parts of Congruent Triangles are Congruent Two triangles are congruent IFF their corresponding parts (angles and sides) are congruent. B C A Q R P A ↔ P; B ↔ Q; C ↔ R Vertices of the 2 triangles correspond in the same order as the triangles are named. Corresponding sides and angles of the two congruent triangles: ≡ ≡ = = │ │ Example:

Congruent Triangles B A C X Y Z ≡ ≡ = = │ │ ∆ABC  ______  A  ____  Z  B  _____  C  ______  Y  X ∆ ZYX ∆ABC  ∆XYZ Note:

Given the following corresponding angles, write a congruence statement. Is there more than one way to write it? If so, list them. R A Y S U N SUNSUN RAYRAY  SUN   RAY Also  NUS   YAR Also  USN   ARY

Proving Triangles Congruent By SSS, SAS, and HL

Included Angles & Sides Included Angle: Included Side: * * * In a triangle, the angle formed by two sides is the included angle for the two sides. The side of a triangle that forms a side of two given angles.

Side-Side-Side SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B C D E F

Side-Angle-Side SAS If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. A BC D E F

Right Triangles In a right triangle, the sides adjacent to the right angle are called the legs. The side opposite the right angle is called the hypotenuse of the right triangle. leg hypotenuse leg

Hypotenuse-Leg HLIf the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. A BC D E F

Decide whether the triangles are congruent. If they are, write a congruence statement

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