Question

Are triangles DEF and LNM similar if LN equals 5 MN equals 3 DE equals 10 and FE equals 6

A. No the corresponding sides are not proportional
B. No the corresponding angles are not congruent
C. Yes by the SSS Similarity Postulate
D. Yes by the SAS Similarity Postulate

Answer 1

D. Yes by SAS Similarity Postulate

Explanation:

This is the answer because if you flip triangle LNM around to shape the DEF. Then you will see that:

1. angle D is congruent to angle L

2. angle E is congruent to angle N

3. angle F is congruent to angle M

4. angle E and N are both 90 degrees

Because (DE and LN) and (MN and FE) are similar and (E and N) are 90 degrees, then we do not need (FD and ML) to tell if triangle DEF and triangle LNM is similar or not. They are similar.

We next need to figure out if the triangles are similar by SSS (Side-side-side) Similarity Postulate or SAS (side-angle-side) Similarity Postulate. The SAS Similarity Postulate states that if you have 2 similar sides and 1 congruent angle, then the two shapes are similar. Right now we have 2 similar sides in (DE and LN) and (MN and FE) and 1 congruent angle that are both 90 degrees. This follows all the rules of the SAS Similarity Postulate, so that means that these two triangles are similar by SAS Similarity Postulate.