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Chapter 4. Congruent Triangles. 4.2 Apply Congruence and Triangles. Congruent figures- They have exactly the same shape. All parts of one figure are congruent to the corresponding parts of the other figure. Corresponding sides and angles are congruent. Example.
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Chapter 4 Congruent Triangles
4.2 Apply Congruence and Triangles • Congruent figures- • They have exactly the same shape. • All parts of one figure are congruent to the corresponding parts of the other figure. • Corresponding sides and angles are congruent.
Example • Name the congruent triangles.
Example • Find x and y.
Third Angle Theorem • If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are also congruent.
4.3 Prove Triangles Congruent by SSS • Side-Side-Side Congruence Postulate- If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the two triangles are congruent.
4.4 Prove Triangles Congruent by SAS and HL • Side- Angle- Side Congruence Postulate – If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, then the 2 triangles are congruent.
Example • R is the center of the circle. Based on the diagram, what can you conclude about ∆URT and ∆SRT ?
Hypotenuse Leg Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the 2 triangles are congruent.
4.5 Prove Triangles Congruent by ASA and AAS • Angle- Side- Angle Congruence Postulate- If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent.
Angle- Angle- Side Congruence Theorem- If 2 angle and a non-included side of one triangle are congruent to 2 angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Right Angle Congruence Theorem- All right angles are congruent.
4.6 Use Congruent Triangles • CPCTC- Corresponding Parts of Congruent Triangles are Congruent