Question

ABCD ≅ FGHJ. Find the measure of the given angles or lengths of the given sides. CD = 2x + 3; HJ = 3x + 2.

Answer 1

The question asks for the length of CD and HJ. To find those, we need to find a connection between them.

In the given statement, it says ABCD ≅ FGHJ. When we look at the equation, the corresponding letters are equal. For example, angle A is congruent to Angle F. Or BC ≅ GH.

So we know that CD and HJ are congruent.
Set them equal:
$2x + 3 = 3x + 2$
Subtract 2x from both sides:
$3 = x + 2$
Subtract 2 from both sides:
$x = 3$
If x is 3, plug it in:
$3(3) + 2$
Simplify:
$9 + 2 = 11$

So, HJ is 11. And because HJ ≅ CD, CD is 11 too.