Question

Which of the following pairs of values for x and y would justify the claim that the two triangles are congruent?

x = 3, y = 11
x = 5, y = 5
x = 7, y = 9
x = 9, y = 7

2 triangles are connected a common side. The length of one side is 2 x + 3. Its corresponding side on the second triangle is 9. The length of another side is y minus 4. Its corresponding side on the second triangle is 7.

Answer 1

Set corresponding sides equal: 2x + 3 = 9 and y − 4 = 7.
Solve: 2x = 6 ⇒ x = 3, and y = 11.

So x = 3, y = 11 (the first pair) makes the two triangles congruent (they then have three equal sides: the two given pairs and the shared side).