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

Question

asked Jun 6, 2018 41.2k views

2 Answers

Thomas John · Answer 1 · 2018-06-12T01:26:48+0000

Answer: FA= 3cm

Explanation:

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

$GHJK\cong ASDF$ and
$GHJK\cong VBNM$

Therefore,
$ASDF\cong VBNM$ (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.