6-3 Proving a Quad is a parallelogram Day 2 Unit 7 6-3 Proving a Quad is a parallelogram

Agenda Warm-Up Homework 6-3 Notes Class Work

Warm-Up In isosceles ABC, <A is the vertex angle. If m<A=2x+6 and m<C=5x-3, find m<B. DEFG is a parallelogram. IF m<G=135, and m<F=2x. Find m<F DEFG is a parallelogram. If EG= 4x+8. H is the midpoint of EG. EH= x + 8. Find EH.

HW Check 125 2. 45 3. 45 4. 130 5. 17 6. 66 7. 66 8. 13 9. 22 10. 30 11. 75 12. 70

6-3 Proving a Quad is a Parallelogram. 5 Ways to Prove a Quad is a Parallelogram: 1. By Definition: If both pairs of opp. sides are ll, then the Quad is a

2. Theorem 6-5: If the diagonals bisect each other, then the Quad is a

3. Theorem 6-6: If one pair of opp 3. Theorem 6-6: If one pair of opp. sides are BOTH ll and , then the Quad is a

4. Theorem 6-7: If both pairs of opp. sides are then the Quad is a

5. Theorem 6-8: If both pairs of opp angles are then the Quad is a

Examples: Can you conclude that the Quadrilateral is a ? If so why? 1. Yes, One pair of opposite sides are parallel and congruent

2. 3. Yes, both pairs of opp sides are parallel due to congruent alternate interior angles. No!

4. 5. No! Yes, opp angles are congruent

6. 7. No! only one pair of parallel sides. 6. 7. No! only one pair of parallel sides. Yes, Diagonals bisect each other.

A B D C Given ABCD is a parallelogram Property of parallelograms Statement Reasons Given ABCD is a parallelogram Property of parallelograms

Homework Worksheet

Homework Check

Class Work Answers 125 2. 45 3. 45 4. 130 5. 17 6. 66 7. 66 8. 13 9. 22 10. 30 11. 75 12. 70