4.6: Congruence in Right Triangles

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Presentation transcript:

4.6: Congruence in Right Triangles

Right Triangles Learning Target: To prove right triangles congruent by the HL Theorem.

Right Triangles Hypotenuse: the longest side of a right triangle Legs: The sides of a right triangle that are not the hypotenuse

Theorem  Theorem 4.6: Hypotenuse-Leg (HL) Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. To use the HL Theorem, you must show that three conditions are met: There are two right triangles The triangles have congruent hypotenuses There is one pair of congruent legs

Using the HL Theorem

Using the HL Theorem Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5.

Using the HL Theorem Statements Reasons 1. 2. 3. 4. 1. 2. 3. 4.

4.6: Congruence in Right Triangles (4.6): Pg. 237; 1-4, 7, 8, 10, 11, 14 p. 234: 1, 3, 5, 8, 9 4.6: Congruence in Right Triangles

Review: Solving Systems

Review: Solving Systems

Review: Solving Systems Find the values of x and y that make the following triangles congruent. 2y+3 x+y x 12