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Understanding the HL Postulate for Proving Right Triangles Congruent

In this lesson, you will learn how to apply the HL (Hypotenuse-Leg) Postulate to demonstrate that two right triangles are congruent. The postulate states that if a correspondence exists between the vertices of two right triangles such that the hypotenuse and one leg of each triangle are congruent, then the triangles are congruent. This lesson also examines how to use this postulate effectively, the conditions for triangle congruence, and provides a summary and homework worksheet to reinforce your understanding.

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Understanding the HL Postulate for Proving Right Triangles Congruent

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  1. 3.8 The HL Postulate Objective: After studying this lesson you will be able to use the HL postulate to prove right triangles congruent.

  2. Postulate: If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent. (HL) E T P N HL is ONLY used with RIGHT TRIANGLES. A C

  3. C Given: A B Prove: D Reason Statement 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9.

  4. Prove: Corresponding angle bisectors of congruent triangles are congruent. Reason Statement 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9.

  5. Given: O O Prove: E G F Reason Statement 1. 2. 3. 4. 5. 6. 7. 1. 2. 3. 4. 5. 6. 7. An altitude of a triangle forms right angles with the side to which it is drawn.

  6. Summary: What type of triangle do we use the HL postulate with? Explain How many conditions are involved with proving two triangles are congruent? Homework: worksheet

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