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Topic: Congruent Triangles (6.0) Objectives Prove triangles are congruent Standards Geometry. Measurement. Problem solving. Reasoning and Proof.

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Presentation on theme: "Topic: Congruent Triangles (6.0) Objectives Prove triangles are congruent Standards Geometry. Measurement. Problem solving. Reasoning and Proof."— Presentation transcript:

1 Topic: Congruent Triangles (6.0) Objectives Prove triangles are congruent Standards Geometry. Measurement. Problem solving. Reasoning and Proof

2 Warm –Up: Classify each triangle. 1. With a 42˚ and a 57˚ angle Acute triangle, the third angle is 81˚, also acute. 2. Two sides are 5 cm long. 3. With two 60˚ angles. Isosceles triangle, two sides are congruent. Equiangular triangle, the third angle is also 60˚.

3 When two geometric figures have the same size and shape, they are said to be congruent. Congruent segments are segments with the Congruent angles are angles with the same length. same measure. CONGRUENCE Congruent triangles are two triangles whose corresponding angles and corresponding sides are the same measure. Triangles have special properties that allow you to prove triangles congruent by identifying only three sets of corresponding parts. Postulates: SSSSASASA AAA Triangles cannot be proven congruent by: SSA called for car trouble. Read it backwards, don’t make one of yourself using this.

4 Postulate 11 The SSS Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Postulate 12 The SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Postulate 13 The ASA Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

5 SSA Two triangles with two sides and a non-included angle equal may or may not be congruent. AAA If two angles on one triangle are equal, respectively, to two angles on another triangle, then the triangles are similar, but not necessarily congruent. Triangles cannot be proven congruent by:

6 Complete the two-column proof: 1. given 2. reflexive property 3. SAS postulate Statements Reasons Given: Prove: 1. 2. 3. N P R Q M

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