Given: ABCD is a rhombus. Prove: ABCD is a parallelogram.

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1 Given: is a rhombus. Prove: is a parallelogram. 1. &. 1. Property of a rhombus Reflexive axiom SSS. + o ( + ) = Interior angle sum for a triangle PT + o ( + ) = Substitution. ( + ) = 7. & are supplementary o-interior angles. 9. Repeat 4 8 to show.

2 Given: is a rhombus. Prove: is a parallelogram. 1. &. 1. Property of a rhombus o ( + ) = Substitution. 7. & are supplementary Repeat 4 8 to show.

3 Given: is a parallelogram. Prove: and bisect each other. 3 E lternate interior angles Opp. Sides of a parallelogram S. 5. E E PT. 7. & bisect each other & 6.

4 Given: is a parallelogram. Prove: and bisect each other. 3 E lternate interior angles lternate interior angles Opp. Sides of a parallelogram. E E S. 5. E E. 5. PT. E E 7. 5 & PT. 7. & bisect each other.

5 Given: is a parallelogram. Prove: Opposite angles are congruent. m + m = Property of o-interior angles. m + m = m + m ancellation ngles with equal measure are cong. 6. Similarly. 6. Steps 1-5.

6 Given: is a parallelogram. Prove: Opposite angles are congruent. m + m = Property of o-interior angles. m + m = Property of o-interior angles. m + m = m + m Substitution. m = m ancellation ngles with equal measure are cong. 6. Similarly. 6. Steps 1-5.

7 Given: is a parallelogram & angle is a right angle. Prove: has all right angles m = Property of a right angle. m + m = Property of o-interior angles m = Substitution Subtraction ngles have equal measure Property of parallelograms ll angles are right angles. 9. ll angles are cong. to angle.

8 Given: is a parallelogram & angle is a right angle. Prove: has all right angles Property of parallelograms. 2. m = Property of a right angle. m + m = Property of o-interior angles m = Substitution. 5. m = Subtraction ngles have equal measure Property of parallelograms Transitive property. 9. ll angles are right angles. 9. ll angles are cong. to angle.

9 Given: is a kite (diagram is to scale). Prove: & bisects &. 1. &. 1. Property of a kite Reflexive axiom SSS & bisects &. 6.

10 Given: is a kite (diagram is to scale). Prove: & bisects &. 1. &. 1. Property of a kite Reflexive axiom SSS PT 5. &. 5. PT 6. bisects &. 6. efinition of angle bisector.

11 Given: is a kite (diagram is to scale). Prove: & bisects. E 1. &. 1. Property/definition of a kite E E SS PT & form a straight line E E 7. bisects. 7. efinition of segment bisector.

12 Given: is a kite (diagram is to scale). Prove: & bisects. E E E 1. &. 1. Property of a kite. 2. E E. 2. Reflexive axiom. E E SS. E E PT & form a straight line. E E 7. efinition of segment bisector PT 7. bisects. E E

13 Given: is a rhombus. Prove: iagonals are perpendicular bisectors. 1. iagonals are perpendicular. 1. rhombus is a kite. 2. iagonals are bisectors. 2. rhombus is a parallelogram. 3. iagonals are perpendicular bisectors. 3. efinition of perpendicular bisector.

14 Given: is a rhombus. Prove: iagonals are perpendicular bisectors. 1. iagonals are perpendicular. 1. rhombus is a kite. 2. iagonals are bisectors. 2. rhombus is a parallelogram. 3. iagonals are perpendicular bisectors. 3. efinition of perpendicular bisector.

15 Given: is a rectangle. Prove: ll interior angles are right angles. 1. One interior angle is a right angle. 1. efinition of a rectangle. 2. ll interior angles are right angles. 2. rectangle is a parallelogram.

16 Given: is a rectangle. Prove: ll interior angles are right angles. 1. One interior angle is a right angle. 1. efinition of a rectangle. 2. ll interior angles are right angles. 2. rectangle is a parallelogram & a parallelogram with one right angle has all right angles.

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