Question

Find the values of x

and y that make these triangles congruent by the HL Theorem.
X = 2, Y = 1
X = 3, y = 2
X=1, y = 2
X = 2, y = 3

Answer 1

9514 1404 393

Answer:

(b) x = 3, y = 2

Explanation:

In order for the triangles to be congruent by the HL theorem, the hypotenuses must be congruent:

3y = x+3

and the corresponding legs must be congruent:

y +1 = x

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We can solve this set of equations by substituting for x:

3y = (y +1) +3

2y = 4 . . . . . . . .subtract y

y = 2 . . . . . . . . .divide by 2

2+1 = x = 3 . . . substitute for y in the equation for x

The solution is (x, y) = (3, 2).