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Given: is a rhombus. Prove: is a parallelogram. Statement Justification 1. &. 1. Property of a rhombus. 2.. 2. Reflexive axiom. 3.. 3. SSS. 4.. 4. Interior.

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Presentation on theme: "Given: is a rhombus. Prove: is a parallelogram. Statement Justification 1. &. 1. Property of a rhombus. 2.. 2. Reflexive axiom. 3.. 3. SSS. 4.. 4. Interior."— Presentation transcript:

1 Given: is a rhombus. Prove: is a parallelogram. Statement Justification 1. &. 1. Property of a rhombus Reflexive axiom SSS Interior angle sum for a triangle CPCTC Substitution. A B CD 7. & are supplementary Co-interior angles. 9. Repeat 4 – 8 to show.

2 Given: is a rhombus. Prove: is a parallelogram. Statement Justification 1. &. 1. Property of a rhombus Substitution. A B CD 7. & are supplementary Repeat 4 – 8 to show.

3 Given: is a parallelogram. Prove: and bisect each other. Statement Justification Alternate interior angles Opp. Sides of a parallelogram ASA CPCTC. 7. & bisect each other &

4 Given: is a parallelogram. Prove: and bisect each other. Statement Justification Alternate interior angles Alternate interior angles Opp. Sides of a parallelogram ASA CPCTC CPCTC. 7. & bisect each other &

5 Given: is a parallelogram. Prove: Opposite angles are congruent. Statement Justification Property of Co-interior angles Cancellation Angles with equal measure are cong. 6. Similarly. 6. Steps 1-5.

6 Given: is a parallelogram. Prove: Opposite angles are congruent. Statement Justification Property of Co-interior angles Property of Co-interior angles Substitution Cancellation Angles with equal measure are cong. 6. Similarly. 6. Steps 1-5.

7 Given: is a parallelogram & angle A is a right angle. Prove: has all right angles. Statement Justification Property of a right angle Property of Co-interior angles Substitution Subtraction Angles have equal measure Property of parallelograms All angles are right angles.9. All angles are cong. to angle A.

8 Given: is a parallelogram & angle A is a right angle. Prove: has all right angles. Statement Justification Property of parallelograms Property of a right angle Property of Co-interior angles Substitution Subtraction Angles have equal measure Property of parallelograms Transitive property. 9. All angles are right angles.9. All angles are cong. to angle A.

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

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

11 Given: is a kite (diagram is to scale). Prove: & bisects. Statement Justification 1. &. 1. Property/definition of a kite SAS CPCTC & form a straight line bisects. 7. Definition of segment bisector.

12 Given: is a kite (diagram is to scale). Prove: & bisects. Statement Justification 1. &. 1. Property of a kite Reflexive axiom SAS CPCTC & form a straight line CPCTC 7. bisects. 7. Definition of segment bisector.

13 Given: is a rhombus. Prove: Diagonals are perpendicular bisectors. Statement Justification 1. Diagonals are perpendicular. 1. A rhombus is a kite. 2. Diagonals are bisectors. 2. A rhombus is a parallelogram. 3. Diagonals are perpendicular bisectors. 3. Definition of perpendicular bisector.

14 Given: is a rhombus. Prove: Diagonals are perpendicular bisectors. Statement Justification 1. Diagonals are perpendicular. 1. A rhombus is a kite. 2. Diagonals are bisectors. 2. A rhombus is a parallelogram. 3. Diagonals are perpendicular bisectors. 3. Definition of perpendicular bisector.

15 Given: is a rectangle. Prove: All interior angles are right angles. Statement Justification 1. One interior angle is a right angle. 1. Definition of a rectangle. 2. All interior angles are right angles. 2. A rectangle is a parallelogram.

16 Given: is a rectangle. Prove: All interior angles are right angles. Statement Justification 1. One interior angle is a right angle. 1. Definition of a rectangle. 2. All interior angles are right angles. 2. A rectangle is a parallelogram & a parallelogram with one right angle has all right angles.


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