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ADVANCED GEOMETRY 3.1/2 What are Congruent Figures? / Three ways to prove Triangles Congruent. Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove that triangles are congruent.

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. In the last chapter, we defined congruent segments and congruent angles. What must be true about congruent segments? What must be true about congruent angles? How many segments does it take to make a triangle? How many angles are in a triangle? So what must be true if two triangles are congruent? A B C D E F

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. In general, two geometric shapes are congruent if one of them can be placed on top of the other and fit exactly, point for point, side for side, angle for angle. Thus, congruent figures have the same _________ and _________. A B C D E F

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. DEFINITION: If two triangles are congruent, then all pairs of corresponding parts (angles and segments) are congruent. If two triangles have all pairs of corresponding parts (angles and segments) congruent, then the triangles are congruent. DEFINITION: If two polygons are congruent, then all pairs of corresponding parts (angles and segments) are congruent. If two polygons have all pairs of corresponding parts (angles and segments) congruent, then the polygons are congruent. Congruent Triangles all pairs of corresponding parts congruent. means "...if and only if..." (reversible statement). means "...implies..." (If...then...).

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. A B C D E F

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A B C D E F G H Given: Conclude:

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent.

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Postulate: Any segment or angle is congruent to itself. (Reflexive Property) E F G H J K AB C D

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent.

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SSS Postulate: If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding three sides of the other triangle, then the two triangles are congruent (SSS ≅ ) A B C D E F

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. SAS Postulate: If there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of the other triangle, then the two triangles are congruent (SAS ≅ ) A B C D E F

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. ASA Postulate: If there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of the other triangle, then the two triangles are congruent (ASA ≅ ) A B C D E F

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent.

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STATEMENTS REASONS

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. STATEMENTS REASONS

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. STATEMENTS REASONS

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. STATEMENTS REASONS

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. STATEMENTS REASONS

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Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent. HW: pg. 114 # 1-3 pg. 120 # 1-4, 6-8

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3-1 Learner Objective: I will identify the corresponding congruent parts of congruent figures and use three triangle congruence postulates to prove triangles congruent.

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