Proof for Theorem
Prove: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent.
Prove: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent.
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Statements |
Reasons |
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1. |
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1. |
Given |
2. |
Draw  |
2. |
Two points determine one line. |
3. |
 |
3. |
Def: A parallelogram is a quad. with 2 pair of opposite sides parallel. |
4. |
 |
4. |
If 2 || lines are cut by a trans., the alternate interior angles are congruent. |
5. |
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5. |
Reflexive (Identity) |
6. |
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6. |
ASA - If 2 angles and the included side of 1 Δ are congruent to the corres. parts of another Δ, the Δs are  . |
7. |
 |
7. |
CPCTC- Corres. parts of Δs are . |
8. |
m∠1=m∠4; m∠2=m∠3 |
8. |
∠s have = measures |
9. |
m∠1+m∠2=m∠3+m∠4 |
9. |
Addition of equalities |
10. |
m∠1 + m∠2 = m∠DAB m∠3 + m∠4 = m∠BCD |
10. |
Angle Addition Postulate (or whole quantity = sum of parts) |
11. |
m∠DAB = m∠BCD |
11. |
Substitution |
12. |
 |
12. |
∠s have = measures |
Instead of using addition, you could also draw the other diagonal
and prepare steps similar to steps 1 through 7.
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