Given: Trapezoid ABCD line AC ≅ line BD Prove: Trapezoid ABCD is isosceles. Fill in the blanks on the two column proof below.

Question

Statements | Reasons

Trapezoid ABCD | 1. ____

line AB || line DC | 2. ____

line AE ⊥ line DC, line BF ⊥ line DC | Construction

3.____ | If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the second.

line AE || line BF | 4. ____

ABFE is a parallelogram | 5. ____

6.____ | Opposite sides of a ▭ are ≅

∠AEC and ∠BED are right angles | 7. ____

8. line AC ≅ line BD | Given

△AEC ≅ △BFD | 9. ___

∠ACE ≅ ∠BDF | 10. ___

11.____ | RPC

12.____ | SAS Postulate

line AD ≅ line BC | 13.____

14._____ | 15._____

Answer 1

Beaux, I have the same question as Paul, who commented on your post. What's preventing you from writing the reasons for the statements? Are you unfamiliar with proofs? Maybe it seems too much like common sense. For example, 1. is just "Given", because you're given the information that ABCD is a trapezoid. For number 2, refer to the definition of a trapezoid. In your book or notes or online or however you're taking the course, you have a definition that states that a trapezoid is a convex quadrilateral with opposite sides ("bases") parallel to each other. So 2. is "Bases of a trapezoid are parallel."

#14 will be what you're trying to prove, which is "ABCD is isosceles".

I hope that helps explain the process! Let me know if you have any more questions...

Geometry rocks!

LizZ.