2.5 Proving Right Triangles Congruent

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Presentation transcript:

2.5 Proving Right Triangles Congruent CHAPTER 2.5 Proving Right Triangles Congruent Copyright © 2014 Pearson Education, Inc.

Theorem 4.6-6 Hypotenuse-Leg (H-L) Theorem Copyright © 2014 Pearson Education, Inc.

Conditions for Using the H-L Theorem To use the H-L Theorem, the triangles must meet three conditions. • There are two right triangles. • The triangles have congruent hypotenuses. • There is at least one pair of congruent legs. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Using the H-L Theorem Given: segment BE bisects segment AD at C Prove: ΔABC ≅ ΔDEC Solution Copyright © 2014 Pearson Education, Inc.

Using Congruent Triangles Statements Reasons Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Other Theorems • Thm 2.13 (Leg-Angle) If a leg and acute angle of one right triangle are congruent to a leg and the corresponding acute angle of another right triangle, then the two right triangles are congruent Proof: Page 109 Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Other Theorems • Thm 2.14 (Leg-Leg) If the two legs of one right triangle are congruent to the two legs of another right triangle, then the two right triangles are congruent Proof: Page 110 Copyright © 2014 Pearson Education, Inc.