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4-6 Congruence in Right Triangles Objective SWBAT prove right triangles congruent using the Hypotenuse-Leg Theorem Important Info In a right triangle, the side ______________ the right angle is called the _______________. It is the ____________ side in the triangle. The other two sides are called the _______. Theorem 4-6 Hypotenuse-Leg (HL) Theorem If the ____________ and a ____ of one right triangle are congruent to the _____________ and a _____ of another right triangle, then they are congruent. Key Concept Conditions for the HL Theorem To use this theorem, the triangle must meet 3 conditions: 1. There are ____ right triangles. 2. The triangles have congruent _____________. 3. There is one pair of congruent _______. Example 1 Using the HL Theorem <ADC and <BDC are right angles and AC = BC. Are triangle ADC and triangle BDC congruent? Explain, and include a picture. Given: <PRS and <RPQ are right angles, SP = QR Prove: Triangle PRS = triangle RPQ S Example 2 Writing a Proof Using the HL Theorem Given: BE bisects AD at C, AB BC, DE EC, AB = DE Prove: Triangle ABC = Triangle DEC B A Given: CD = EA, AD is the perpendicular bisector or CE Prove: Triangle CBD = triangle EBA A Homework ___________________________ P Q R D C E C B E D