Proof for Theorem
Prove: If a parallelogram is a rhombus, it has diagonals bisecting the angles.
Prove: If a parallelogram is a rhombus, it has diagonals bisecting the angles.
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Statements |
Reasons |
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1. |
rhombus ABCD |
1. |
Given |
2. |
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2. |
A rhombus is a parallelogram with 4 congruent sides. |
3. |
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3. |
A rhombus is a parallelogram with 4 congruent sides. |
4. |
Isos. ΔADC, ΔDCB, ΔCBA, ΔBAD |
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Isos. triangle has 2  sides. |
5. |
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5. |
Base ∠s of an isosceles triangle are congruent. |
6. |
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6. |
Diagonal of a parallelogram forms two congruent triangles.
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7. |
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7. |
CPCTC - corres. parts of triangles are . |
8. |
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8. |
Transitive property |
9. |
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9. |
An angle bisector is a ray in the interior of the ∠ forming 2 ∠s. |
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