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

D C Statement Justification & 1. Property of a rhombus. 2. Reflexive axiom. 3. SSS. 4. Interior angle sum for a triangle. 5. CPCTC 6. Substitution. & are supplementary. 8. Co-interior angles. 9. Repeat 4 – 8 to show

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

D C Statement Justification & 1. Property of a rhombus. 2. 3. 4. 5. 6. 6. Substitution. & are supplementary. 7. 8. 8. 9. Repeat 4 – 8 to show

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**Given: is a parallelogram. Prove: and bisect each other.**

2 3 4 1 Statement Justification 1. Alternate interior angles. 3. Opp. Sides of a parallelogram. 4. ASA. 6. CPCTC. & bisect each other. & 6.

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**Given: is a parallelogram. Prove: and bisect each other.**

2 3 4 1 Statement Justification 1. Alternate interior angles. 2. Alternate interior angles. 3. Opp. Sides of a parallelogram. 4. ASA. 5. CPCTC. 6. CPCTC. & bisect each other. & 6.

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**Given: is a parallelogram. Prove: Opposite angles are congruent.**

Statement Justification 2. Property of Co-interior angles. 4. Cancellation. 5. Angles with equal measure are cong. 6. Similarly 6. Steps 1-5.

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**Given: is a parallelogram. Prove: Opposite angles are congruent.**

Statement Justification 1. Property of Co-interior angles. 2. Property of Co-interior angles. 3. Substitution. 4. Cancellation. 5. Angles with equal measure are cong. 6. Similarly 6. Steps 1-5.

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**Given: is a parallelogram &. angle A is a right angle**

Given: is a parallelogram & angle A is a right angle. Prove: has all right angles. Statement Justification 2. Property of a right angle. 3. Property of Co-interior angles. 4. Substitution. 5. Subtraction. 6. Angles have equal measure. 7. Property of parallelograms. 9. All angles are right angles. 9. All angles are cong. to angle A.

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**Given: is a parallelogram &. angle A is a right angle**

Given: is a parallelogram & angle A is a right angle. Prove: has all right angles. Statement Justification 1. Property of parallelograms. 2. Property of a right angle. 3. Property of Co-interior angles. 4. Substitution. 5. Subtraction. 6. Angles have equal measure. 7. Property of parallelograms. 8. Transitive property. 9. All angles are right angles. 9. All angles are cong. to angle A.

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**Given: is a kite (diagram is to scale). Prove: & bisects & .**

Statement Justification & 1. Property of a kite. 2. Reflexive axiom. 3. SSS. 4. & 5. bisects & 6.

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**Given: is a kite (diagram is to scale). Prove: & bisects & .**

Statement Justification & 1. Property of a kite. 2. Reflexive axiom. 3. SSS. 4. CPCTC & 5. CPCTC bisects & 6. Definition of angle bisector.

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**Given: is a kite (diagram is to scale). Prove: & bisects .**

Statement Justification & 1. Property/definition of a kite. 2. 3. SAS. 4. CPCTC & form a straight line. 6. bisects 7. Definition of segment bisector.

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**Given: is a kite (diagram is to scale). Prove: & bisects .**

Statement Justification & 1. Property of a kite. 2. Reflexive axiom. 3. SAS. 4. CPCTC & form a straight line. 6. CPCTC bisects 7. Definition of segment bisector.

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**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.

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**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.

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**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.

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**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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SECTION 8-2, 8-4, 8-5 spi.3.2.H Jim Smith JCHS. Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD A B CD › › › › › ›

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