(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

segment EG over segment LN equals segment FG over segment MN

Step-by-step 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

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

Step-by-step explanation:

We are given that 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

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.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

a

step-by-step explanation: