4.9 (M1) Prove Triangles Congruent by SAS & HL

1. 4.9 (M1) Prove Triangles Congruent by SAS & HL

2. Vocabulary • In a right triangle, the sides adjacent to the right angle are the legs. • The side opposite the right angle is the hypotenuse. • Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.

3. Hypotenuse-Leg (HL) Congruence Theorem – If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent.

4. Tell whether the pair of triangles is congruent or not and why. Yes; HL Thm. ANSWER

5. 1. ABE,CBD ANSWER SAS Post. Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

6. 2. FGH,HJK ANSWER HL Thm. Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

7. State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate. 3. ST YZ, RS XY ANSWER SY.

8. BC DA,BC AD ABCCDA ABCCDA STATEMENTS REASONS S BC DA Given Given BC AD BCADAC A Alternate Interior Angles Theorem S ACCA Reflexive Property of Congruence EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN PROVE 5. SAS

9. WYZXZY PROVE Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram. EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof. GIVEN WY XZ,WZ ZY, XY ZY SOLUTION

10. STATEMENTS REASONS WY XZ Given WZ ZY, XY ZY Given Definition of lines Z andY are right angles Definition of a right triangle WYZand XZY are right triangles. ZY YZ L Reflexive Property of Congruence WYZXZY HL Congruence Theorem EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem