Question

Match the reasons to the statements given.

Given:
ABCD
EF contains T
Prove:
ET = FT

Answer 1

Answer:

The reasons and the statements are given as follows;

1. Parallelogram ABCD             ${}$                 Given

2. BT = TD            ${}$                 Diagonals of parallelogram bisect each other

3. ∠1 = ∠2            ${}$                  Vertically opposite angles

4. BC ║ AD             ${}$               Definition of parallelogram

5. ∠3 = ∠4            ${}$                  If lines are parallel then alternate interior

                                               angles are equal

6. Triangle BET congruent to Triangle DFT by ASA

7. ET = T_F             ${}$                  CPCTE

Step-by-step explanation:

Statement             ${}$                 Reason

1. Parallelogram ABCD          The given quadrilateral

2. BT = TD Based on the properties of a parallelogram, the parallelogram diagonals bisect each other

3. ∠1 = ∠2  Vertically opposite angles formed by two intersecting lines are equal

4. BC ║ AD By definition, the opposite sides of a parallelogram are parallel

5. ∠3 = ∠4  Based on the property of equality of the alternate interior angles of two parallel lines

6. Triangle BET congruent to Triangle DFT by Angle-Side-Angle rule of congruency

7. ET = T_F by Congruent Parts of Congruent Triangles are Equal, CPCTE, postulate.

Answer 2

The reasons that matches the statements in the two-column proof is shown in the table attached in the image below.

Recall:

• Based on the, CPCTE Theorem, if two triangles are congruent, all its corresponding sides and angles of both triangles are therefore congruent together.
• The ASA Congruent Theorem justifies that two triangles are congruent if they have two pairs of congruent angles and a pair of included sides that are also congruent.

Given parallelogram ABCD, and also, we know that EF contains T, to prove that ET = FT, establish that:

ΔBET ≅ ΔDFT by the ASA Congruence Theorem, then demonstrate that ET = FT by the CPCTE Theorem.

Therefore, the reasons that matches the statements in the two-column proof is shown in the table attached in the image below.

Learn more about ASA Congruence Theorem on:

https://brainly.com/question/3168048