Proof for Theorem
Prove: If a trapezoid has it opposite angles supplementary, it is an isosceles trapezoid.
thisos6given
 isos6pf
 
Statements
  
Reasons
1.
trap. ABCD
∠A supp ∠C; ∠B supp ∠D
1.
Given
2.
thisos2pf3
2.
A trap. is a quad. with at least 1 pr. of parallel sides.
3.
∠A supp ∠D
∠B supp ∠C
3.
If 2 || lines are cut by a trans., the int. ∠s on same side of transversal are supp.
4.
∠D congruent∠C
∠A congruent ∠B
4.
Supplements of the same ∠ , or congruent ∠s, are congruent.
5.
isos. trap. ABCD
5.
An isos. trap. is a trap. with congruent base angles.

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