Proof for Theorem
Prove: If a quadrilateral (with one set of parallel sides) is an isosceles trapezoid, its legs are congruent.

thisospf1given
thisos1
 
Statements
  
Reasons
1.
isos. trap. ABCD
1.
Given
2.
∠Acongruent∠B
2.
An isos. trap. is a trapezoid with congruent base angles.
3.
Draw thisso2pf3
3.
From a given point not on a given line, only one ⊥ can be drawn.
4.
∠DPA, ∠CQB right ∠
4.
Perpendicular lines meet to form right angles.
5.
∠DPA congruent ∠CQB
5.
All right ∠s are congruent.
6.
DP = CQ
6.
Parallel lines are everywhere equidistant.
7.
thisos1pf7
7.
congruentsegments have = measure.
8.
thisso1pf6
8.
AAS - if 2 ∠s and the non-included side of 1Δ are congruent to the corres. parts of another Δ, the Δs are congruent.
9.
thisos1pf9
9.
CPCTC-corres. partscongruentΔs arecongruent.

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