Question

Suppose side TM≅side GL and ∠M ≅ ∠G. What additional information is needed to prove triangle MTD≅GLS by SAS?

side MD≅side SG
∠T≅∠L
side TD≅side SL
∠T≅∠S

Answer 1

Hello there.

Suppose side TM≅side GL and ∠M ≅ ∠G. What additional information is needed to prove triangle MTD≅GLS by SAS?

side MD≅side SG

Answer 2

Option (1) is correct.

For MTD ≅ GLS by SAS similarity criterion, side MD ≅ side SG in additional to given information.

Explanation:

Given two triangles, ΔMTD and ΔGLS,

Also, given

side TM ≅ side GL

and ∠M ≅ ∠G

We need to prove that MTD ≅ GLS by SAS similarity criterion.

SAS similarity criterion states when two sides and angle between those two sides are equal then both the triangles are similar to each other.

Thus, for the given two triangles to be similar,

Since ∠M lies in between sides TM and DM and ∠G lies in between sides SG and GL .

So , for one more pair of equal sides, we will consider side MD ≅ side SG

Thus, for MTD ≅ GLS by SAS similarity criterion. side MD ≅ side SG in additional to given information.

Option (1) is correct.