Question

1. use figure 4 to prove that $\triangle wxy cong \triangle wzy$. (segments $xy$ and $zy$ are tangent to circle $w$.)

Explanation:

Step1: Identify radii of circle W

$WX = WZ$ (Radii of the same circle are congruent)

Step2: Identify tangent properties

$\angle WXY = \angle WZY = 90^\circ$ (A tangent to a circle forms a right angle with the radius at the point of contact)

Step3: Identify common side

$WY = WY$ (Reflexive property of congruence, side is common to both triangles)

Step4: Apply HL congruence rule

For right triangles $\triangle WXY$ and $\triangle WZY$: we have a pair of congruent legs ($WX=WZ$) and a congruent hypotenuse ($WY=WY$). By the Hypotenuse-Leg (HL) congruence theorem for right triangles, the triangles are congruent.

Answer:

$\triangle WXY \cong \triangle WZY$ is proven by the HL congruence theorem for right triangles.