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

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,

When I answered this before, you said you weren't sure about what to use as reasons. You have been given (in class, online, in a book, somewhere) a variety of definitions of angles, shapes, relationships between lines, etc. Rely on these. For example, if you wanted to state from a picture that "polygon ABC is a triangle", check your definition of "triangle" and prove that ABC has the three sides, or three angles, or 180^o, or whatever your definition says.

If you're sitll having trouble, and your teacher can't help, hire a tutor. Khanacademy.org is also a great resource, but you have to put time in to learn the skills and do the exercises.

Take good notes in math class, and good luck with this!

Liz Z.