# ABCD   FGHJ. Find the measure of the given angles or lengths of the given sides. CD = 2x + 3; HJ = 3x + 2. Will all of the triangles be congruent? these two are part of the same question please...

1. ABCD   FGHJ. Find the measure of the given angles or lengths of the given sides. CD = 2x + 3; HJ = 3x + 2. Will all of the triangles be congruent?

these two are part of the same question please explain the answer.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The problem does not provide as much information as the questions of problem need.

If the triangles the problem refers to are the triangles formed by diagonals of 4 sided polygons then you need to specify it, because there is an infinite number of possibilities of drawing triangles in the given 4 sided polygons.

Considering these triangles as those formed by diagonals, then they are congruent if only 4 sided polygons are congruent.

If all the lengths of  each of 4 sided polygons are equal, then they are squares or rhombus.

You may find the lengths of each 4 sided polygons considering the congruence condition CD=HJ.

Substituting the equation 2x + 3 for CD and 3x + 2 for HJ yields:

2x + 3 = 3x + 2 => 2x - 3x = 2 - 3 => -x = -1 => x = 1

You need to substitute 1 for x in 2x + 3 and 3x + 2 such that:

CD = 2 + 3 = 5 units => by congruence yields that HJ = 5 units.

Hence, evaluating the lengths of CD and HJ yields that they measure 5 units each.