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4.4 - Prove Triangles Congruent by SAS and HL Included Angle: Angle in-between two congruent sides 1. Use the diagram to name the included angle between the given pair of sides. GH and HI H 1. Use the diagram to name the included angle between the given pair of sides. HI and IG HIG 1. Use the diagram to name the included angle between the given pair of sides. JG and IG JGI 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 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS 2. Decide whether the triangles are congruent. Explain your reasoning. No, AD ≠ CD 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, HL 2. Decide whether the triangles are congruent. Explain your reasoning. No, Not a right triangle 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS 3. State the third congruence that must be given to prove ABC DEF. BA ______. ED GIVEN: B E, BC EF , ______ Use the SAS Congruence Postulate. 3. State the third congruence that must be given to prove ABC DEF. DF AC ______. GIVEN: AB DE , BC EF , ______ Use the SSS Congruence Postulate. 3. 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 4. Given: G is the midpoint of RT and HI Prove: ∆RGI ∆TGH 1. G is the midpoint of RT 2. RG GT 3. HG GI 4. RGI TGH 5. ∆RGI ∆TGH and HI 1. given 2. Def. of midpt 3. Def. of midpt 4. Vertical angles 5. SAS A 5. Given: Prove: AB CD AB CD ∆ABD ∆CDB Statements 1. AB CD B D C Reasons 1. Given A B D C 5. Given: A AB CD AB CD Prove: D ∆ABD ∆CDB Statements 1. B AB CD Reasons 1. Given 2. CDB ABD 2. 3. AB CD 3. Given 4. DB DB 4. Reflexive 5. ∆ABD ∆CDB 5. SAS C Alternate Interior Angles A 6. Given: AC bisects DAB DA BA Prove: ∆ACD ∆ACB Statements D C B 1. AC bisects DAB Reasons 1. Given 2. DAC BAC 2. Def. of Angle Bisector 3. DA BA 3. Given 4. AC AC 4. Reflexive 5. ∆ACD ∆ACB 5. SAS A 7. Given: AD AB AC BD Prove: ∆ACD ∆ACB Statements 1. AD AB 2. AC BD 3. ACD and ACB are D C B Reasons 1. Given 2. Given 3. Def. of perp. lines right angles 4. ACD ACB 5. AC AC 4. All right angles are 6. ∆ACD ∆ACB 6. HL 5. Reflexive HW Problem 4.4 243 1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38 # 26 Ans: AB DE