Question

question 27 of 28
according to the diagram below, △tsu≅△klm by ha. we know that ∠t≅∠k because they are both right - angles. which of the following theorems can also show congruence?
a. aas
b. sss
c. la
d. sas

Explanation:

Step1: Analyze given information

We have right - angled triangles $\triangle TSU$ and $\triangle KLM$ with $\angle T=\angle K = 90^{\circ}$ and one hypotenuse - leg congruence (HA). Also, from the diagram, we can see that the non - right angles and the other leg can be considered.

Step2: Recall congruence theorems

AAS (Angle - Angle - Side) requires two angles and a non - included side. SSS (Side - Side - Side) requires all three sides. LA (Leg - Angle) is applicable for right - angled triangles. SAS (Side - Angle - Side) requires two sides and the included angle.

Step3: Determine applicable theorem

Since we have right - angled triangles, a right angle, and a leg (the marked equal sides) and another non - right angle (the non - right angles in right - angled triangles), the LA (Leg - Angle) theorem can be used to show congruence.

Answer:

C. LA