Question

what values of y and z make δstu ≅ δigh?
s
18
t
y+41
i
z+11
g
46
h
y =

z =

Explanation:

Step1: Find y using congruent sides

Since \(\triangle STU \cong \triangle IGH\), corresponding sides are equal. The hypotenuse \(SU\) (length \(y + 41\)) corresponds to \(IH\) (length \(46\)). So we set up the equation:
\(y + 41 = 46\)
Subtract 41 from both sides:
\(y = 46 - 41\)
\(y = 5\)

Step2: Find z using congruent sides

The leg \(ST\) (length \(18\)) corresponds to \(IG\) (length \(z + 11\)). So we set up the equation:
\(z + 11 = 18\)
Subtract 11 from both sides:
\(z = 18 - 11\)
\(z = 7\)

Answer:

\(y = 5\), \(z = 7\)