Three quadrilaterals exist such that ghjk ≅ asdf and ghjk ≅ vbnm. if mv measures 3 cm, which other segment must measure 3 cm? -a f -kj -fd -gj

FA= 3cm

Explanation:

Here, three quadrilaterals GHJK,ASDF  and GHJK are given such that,  

and

Therefore, (by transitive property of congruence)

And, if two shapes are congruent to each other then there corresponding sides and angles must be congruent.

That is, In quadrilaterals  ASDF and VBNM, edges AS, SD, DF and FA are corresponding to VB, BN, NM and MV respectively.

Therefore, FA=MV

But, MV= 3 cm ⇒FA=3cm.

Thus, Option (1) is correct.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have