Question

3 look at the figure. find y.

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since the two right - angled triangles \( \triangle VST\) and \( \triangle VTU\) have a common hypotenuse \(VT\) and the angles at \(V\) are equal (given), by the Hypotenuse - Leg (HL) Congruence Theorem, the two triangles are congruent. Then their corresponding sides are equal. So, \(5y=3y + 6\).

Step2: Solve the equation for \(y\)

Subtract \(3y\) from both sides of the equation \(5y=3y + 6\).
We get \(5y-3y=3y + 6-3y\), which simplifies to \(2y=6\).
Divide both sides by 2: \(y=\frac{6}{2}\).

Answer:

\(3\)