Question

I'm not really good at math as you guys can tell... sorry

Answer 1

1) Parallelogram ABCD ---------------> Given

2) BT = TD ---------------------------------> Diagonals of a parallelogram bisect

3) <1 = <2 ----------------------------------> Vertical angles are equal

4) BC ║ AD -------------------------------> Definition of parallelogram

5) <3 = <4 ---------------------------------> If lines parallel, then alternate interior angles are equal

6) Triangle BET congruent to Triangle DFT ------>ASA

7) ET = TF ---------------------------------> CPCTE

Hope they help.

Answer 2

The statements with accurate reasons are show below.

Explanation:

Given: ABCD is a parallelogram, EF contains T.

Prove: ET=FT

1. Parallelogram ABCD (Given)

2. BT=TD (Diagonals of a parallelogram bisect each other)

3. ∠1=∠2 (Vertical angles are equal)

4. BC║AD (Definition of parallelogram)

5. ∠3=∠4 (If lines parallel, then alternate interior angles are equal)

Two corresponding angles and their included sides are congruent. So, by ASA both ΔBET and ΔD FT are congruent.

6. ΔBET ≅ ΔD FT (ASA)

7. ET=T F (CPCTE)