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**4.4 (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. 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.

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**Is there enough given information to prove the triangles congruent**

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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**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 BC DA, BC AD PROVE ABC CDA STATEMENTS REASONS Given BC DA S Given BC AD BCA DAC Alternate Interior Angles Theorem A AC CA Reflexive Property of Congruence S ABC CDA 5. SAS

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**Complete in your notebooks**

3-11, 20, 21, 35

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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.

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**Tell whether the pair of triangles is congruent or not and why.**

ANSWER Yes; HL Thm.

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**Is there enough given information to prove the triangles congruent**

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

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

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**Extra Practice Complete in your notebooks.**

Page ,22, 31, 32, 34

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1 MM1G3c Proving Triangles Congruent (AAS, HL). 2 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding.

1 MM1G3c Proving Triangles Congruent (AAS, HL). 2 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding.

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