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4.4 - Prove Triangles Congruent by SAS and HL Included Angle: Angle in-between two congruent sides Side-Angle-Side (SAS) Congruence Postulate E A 4cm AB CD A C AE CF F B C 4cm D included If two sides and the _____________ angle of congruent to two sides and one triangle are __________ the included angle of a second triangle, then the congruent two triangles are ____________ Right Triangles: hypotenuse leg leg Hypotenuse-Leg (HL) Congruence Theorem: hypotenuse If the _______________ and a ________ of a leg right congruent ___________ triangle are ____________ to the _____________ of a second hypotenuse and ________ leg _________ right triangle, then the two triangles are _________________. congruent Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS Decide whether the triangles are congruent. Explain your reasoning. No, AD ≠ CD Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS Decide whether the triangles are congruent. Explain your reasoning. Yes, HL Decide whether the triangles are congruent. Explain your reasoning. No, Not a right triangle Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS 2. State the third congruence that must be given to prove ABC DEF. BA ______. ED GIVEN: B E, BC EF , ______ Use the SAS Congruence Postulate. 2. State the third congruence that must be given to prove ABC DEF. DF AC ______. GIVEN: AB DE , BC EF , ______ Use the SSS Congruence Postulate. 2. State the third congruence that must be given to prove ABC DEF. GIVEN: AC DF , A is a right angle and A D. Use the HL Congruence Theorem. BC EF A Given: Prove: AB CD AB CD ∆ABD ∆CDB Statements AB CD B D C Reasons Given A B D C Given: Prove: A AB CD AB CD ∆ABD ∆CDB B D C Statements Reasons AB CD Given CDB ABD Alternate Interior Angles AB CD Given DB DB Reflexive ∆ABD ∆CDB SAS Given: RI TH G is the midpoint of HI RGI is a right angle Prove: ∆RGI ∆TGH 1. 2. 3. 4. 5. 6. RI TH 1. G is the midpoint of HI 2. 3. HG GI RGI is a right angle 4. TGH is a right angle 5. RGI & TGH are right 6. given given Def. of midpt given Vertical angles Def. of right triangles triangles 7. ∆RGI ∆TGH 7. HL