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4.9 (M1) Prove Triangles Congruent by SAS & HL

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Vocabulary In a right triangle, the sides adjacent to the right angle are the legs. In a right triangle, the sides adjacent to the right angle are the legs. The side opposite the right angle is the hypotenuse. 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. 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.

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

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

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Daily Homework Quiz For use after Lesson 4.4 Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem. 1. ABE, CBD ANSWER SAS Post.

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Daily Homework Quiz For use after Lesson 4.4 Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem. 2. FGH, HJK ANSWER HL Thm.

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Daily Homework Quiz For use after Lesson 4.4 State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate. 3. ST YZ, RS XY ANSWER S Y.

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EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN PROVE STATEMENTS REASONS BC DA, BC AD ABC CDA 1. Given 1. BC DA S Given 2. BC AD 3. BCA DAC 3. Alternate Interior Angles Theorem A 4. AC CA Reflexive Property of Congruence S 5. ABC CDA 5. SAS Congruence Post.

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

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STATEMENTS REASONS EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem 1. WY XZ 1. Given 4. Definition of a right triangle WYZ and XZY are right triangles. L ZY YZ 5. Reflexive Property of Congruence 6. WYZ XZY 6. HL Congruence Theorem 3. Definition of lines Z and Y are right angles 2. WZ ZY, XY ZY Given

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