Unit 4 Lesson 3 Prove Triangles Congruent by

Unit 4 Lesson 3 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. H

1. Use the diagram to name the included angle between the given pair of sides. HIG

1. Use the diagram to name the included angle between the given pair of sides. JGI

Side-Angle-Side (SAS) Congruence Postulate E A 4 cm F B C 4 cm D

included If two sides and the _______ angle of one congruent triangle are _____ to two sides and the included angle of a second triangle, then the congruent two triangles are ______

Right Triangles: leg hypotenuse 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 _____ triangle, then the two right 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 third congruence that must be given to prove ABC DEF. GIVEN: B E, , ______. Use the SAS Congruence Postulate.

3. State third congruence that must be given to prove ABC DEF. GIVEN: , ______. Use the SSS Congruence Postulate.

3. State third congruence that must be given to prove ABC DEF. GIVEN: A is a right angle and A D. Use the HL Congruence Theorem.

4. Given: Prove: ∆RGI ∆TGH 1. 2. 3. 4. RGI TGH 5. ∆RGI ∆TGH 1. given 2. Def. of midpt 3. Def. of midpt 4. Vertical angles 5. SAS

A 5. Given: B D Prove: ∆ABD ∆CDB Statements 1. C Reasons 1. Given

A B D C

A 5. Given: B D Prove: ∆ABD ∆CDB Statements 1. Reasons 1. Given 2. CDB ABD 2. 3. Given 4. Reflexive 5. ∆ABD ∆CDB 5. SAS C Alternate Interior Angles

A 6. Given: Prove: ∆ACD ∆ACB Statements D C B 1. Reasons 1. Given 2. Def. of Angle Bisector 3. Given 4. Reflexive 5. ∆ACD ∆ACB 5. SAS

A 7. Given: Prove: ∆ACD ∆ACB Statements 1. 2. 3. ACD and ACB are right angles D C B Reasons 1. Given 2. Given 3. Def. of perp. lines 4. 5. 4. All right angles are 6. ∆ACD ∆ACB 6. HL 5. Reflexive

HW Problem LT Assignment 3. 2 and 3. 3 3 -7 odd, 9 -11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all) # 27 Ans: Due