Question

(easy) If ΔEFG ~ ΔLMN with a ratio of 3:1, which of the following is true?

segment EG is congruent to segment LM
segment EF is congruent to segment LM
segment EG over segment LN equals segment FG over segment MN
segment EF over segment LM equals segment EG over segment LM

Answer 1

C: Segment EG over segment LN equals segment FG over MN.

Explanation:

We are given that
`\triangle EFG \sim\traingle LMN` with ratio 3:1

We have to find the true statement about two similar triangles in given options

When two triangle are similar

Then ratios of all sides of one triangle to its corresponding all sides of another triangle are equal.

Therefore, Corresponding side of EF is LM

Corresponding side of FG is MN

Corresponding side of EG is LN

Ratio

`(EF)/(LM)=(FG)/(MN)=(EG)/(LN)=(3)/(1)`

Hence, segment FG over segment MN equals to segment EG over segment LN.

Therefore, option C is true.

Answer : C: Segment EG over segment LN equals segment FG over MN.

Answer 2

segment EG over segment LN equals segment FG over segment MN

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

EF and LM

EG and LN

FG and MN

The corresponding angles are

∠E≅∠L

∠F≅∠M

∠G≅∠N

therefore

EF/LM=EG/LN=FG/MN=3/1