Question

triangles kts and hmw are shown, where hm ⊥ wm, sk ≅ hn, and ts ≅ wh. complete the statement. △kts is congruent to △hmw congruent to △mhw congruent to ∠whm not congruent to ∠mwh because

Explanation:

Step1: Identify the given congruent sides

We are given \(SK\cong HN\) and \(TS\cong WH\).

Step2: Identify the right angles

Since \(HM\perp WM\), \(\angle HMW = 90^{\circ}\). In \(\triangle KTS\), assume the angle at \(T\) (if we consider the right - triangle property based on the congruence context) is also a right angle (by the nature of the problem setup with the given side - side - right - angle congruence).

Step3: Apply the HL congruence criterion

For right - triangles, if the hypotenuse (\(SK\cong HN\)) and one leg (\(TS\cong WH\)) are congruent, then the triangles are congruent. So, \(\triangle KTS\cong\triangle HMW\) by the Hypotenuse - Leg (HL) congruence criterion.

Answer:

\(\triangle KTS\cong\triangle HMW\) because \(SK\cong HN\), \(TS\cong WH\), and \(\angle HMW\) and \(\angle KTS\) are right angles (since \(HM\perp WM\)). By the Hypotenuse - Leg (HL) congruence criterion for right - triangles.