Question

Find the values of x and ​y​ for which △ABC and △XYZ are congruent.​ABC​: side lengths of 4x+3, 5, and ​8y−1

​XYZ​: side lengths of ​6x−1, 5, and y+6
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Answer 1

Answer: Two triangles are congruent if and only if all corresponding sides are equal in length. So, to find the values of x and y for which ΔABC and ΔXYZ are congruent, we need to equate the corresponding side lengths:

4x + 3 = 6x - 1

5 = 5

8y - 1 = y + 6

Solving the first equation for x:

4x + 3 = 6x - 1

2x = -4

x = -2

Solving the third equation for y:

8y - 1 = y + 6

7y = 7

y = 1

So, the values of x and y that make ΔABC and ΔXYZ congruent are x = -2 and y = 1.

Explanation: