Question

WHAT IN THE WORLD IS ΔLIT ≅ ΔTER

Answer 1

`$\overline{LT}\cong\overline{TR}$` (Given) ;
`$\angle ILT\cong\angle ETR$` (Given);
`$IT||ER$` (Alternate Interior Angles);
`$\angle LTI\cong\angle ERT$` (Corresponding Angles)and
`$\triangle LIT\cong\triangle TER$` (ASA). The prove is done below.

The correct reasons for each statement in the proof are as follows:

Statements| Reasons

1.
`$\overline{LT}\cong\overline{TR}$` | Given

2.
`$\angle ILT\cong\angle ETR$` | Given

3.
`$IT||ER$` | Alternate Interior Angles

4.
`$\angle LTI\cong\angle ERT$` | Corresponding Angles

5.
`$\triangle LIT\cong\triangle TER$`| ASA

Explanation:

Step 1: We are given that
`$\overline{LT}\cong\overline{TR}$`.

Step 2: We are also given that
`$\angle ILT\cong\angle ETR$`.

Step 3: Since
`$\overline{LT}\cong\overline{TR}$` and
`$\overline{IT}\cong\overline{ER}$` (they are both opposite to the corresponding equal sides), we can conclude that
`$\triangle ILT$` and
`$\triangle ETR$` are similar. Therefore,
`$\angle LTI\cong\angle ERT$` (corresponding angles of similar triangles are congruent).

Step 4: Now we have that
`$\overline{LT}\cong\overline{TR}$`,
`$\angle ILT\cong\angle ETR$`, and
`$\angle LTI\cong\angle ERT$`. Therefore,
`$\triangle LIT\cong\triangle TER$` by the ASA Congruence Theorem (two triangles are congruent if they have two congruent angles and a congruent side between them).

The probable question is attached below.