Question

Figure ABCD was translated and resulted in image A'B'C'D'.

Answer 1

Step-by-step explanation:

+) Polygons ABCD has: A(-7;4); B(-5;7); C(-3;4); D(-5; 1)

+) Polygons A'B'C'D' has: A'(-9;0); B'(-7;3); C'(-5;0); D'(-7;-3)

The side lengths of ABCD:

$AB = \sqrt{[-7-(-5)]^{2}+(4-7)^{2} } = \sqrt{13}$

$BC = \sqrt{[-3-(-5)]^{2}+(7-4)^{2} } =\sqrt{13}$

$CD = \sqrt{[-5-(-3)]^{2}+(1-4)^{2} } =\sqrt{13}$

$DA = \sqrt{[-7-(-5)]^{2}+(4-1)^{2} } =\sqrt{13}$

The side lengths of A'B'C'D':

$A'B' = \sqrt{[-7-(-9)]^{2}+(3-0)^{2} } = \sqrt{13}$

$B'C' = \sqrt{[-5-(-7)]^{2}+(0-3)^{2} } =\sqrt{13}$

$C'D' = \sqrt{[-7-(-5)]^{2}+(-3-0)^{2} } =\sqrt{13}$

$D'A' = \sqrt{[-9-(-7)]^{2}+[0-(-3)]^{2} } =\sqrt{13}$

So that side lengths of ABCD equal to those of A'B'C'D'.

However, this is not enough to said that they are congruent polygons, as 2 polygons are congruent when they have all corresponding sides and interior angles are congruent.

ABCD and A'B'C'D' have all corresponding sides congruent.

=> So that "all corresponding interior angles are congruent" must be true for them to be congruent polygons