Question

which of the following statements do not show that the right triangles are congruent?
$overline{km}congoverline{rt}$ and $overline{kl}congoverline{rs}$
$overline{lm}congoverline{st}$ and $overline{kl}congoverline{rs}$
$angle kcongangle r$ and $angle lcongangle s$
$overline{km}congoverline{rt}$ and $angle kcongangle r$

Explanation:

Step1: Recall congruence criteria for right - triangles

For right - triangles, we have criteria like \(HL\) (Hypotenuse - Leg), \(LL\) (Leg - Leg), \(LA\) (Leg - Angle).

Step2: Analyze each option

• For \(\overline{KM}\cong\overline{RT}\) and \(\overline{KL}\cong\overline{RS}\): This is \(LL\) (Leg - Leg) congruence for right - triangles.
• For \(\overline{LM}\cong\overline{ST}\) and \(\overline{KL}\cong\overline{RS}\): This is \(LL\) (Leg - Leg) congruence for right - triangles.
• For \(\angle K\cong\angle R\) and \(\angle L\cong\angle S\): Just having two pairs of congruent angles (AAA) does not prove triangle congruence. In the case of right - triangles, we need at least one pair of corresponding sides to be congruent.
• For \(\overline{KM}\cong\overline{RT}\) and \(\angle K\cong\angle R\): This is \(LA\) (Leg - Angle) congruence for right - triangles.

Answer:

\(\angle K\cong\angle R\) and \(\angle L\cong\angle S\)