Question

using the diagram shown, choose the correct conclusion. the triangles are congruent by hl. the triangles are congruent by la. the triangles are congruent by ha. there is not enough information to determine whether the triangles are congruent.

Explanation:

Step1: Recall congruence criteria for right - angled triangles

For right - angled triangles, we have several congruence criteria: HL (Hypotenuse - Leg), LA (Leg - Angle), HA (Hypotenuse - Angle).

Step2: Analyze the given information

We know that both triangles are right - angled (right angle is one of the angles). We are given that one of the non - right angles ($20^{\circ}$) is equal in both triangles and the legs (the sides adjacent to the $20^{\circ}$ angle) are equal (marked with the same tick).

Step3: Apply the LA criterion

The LA (Leg - Angle) congruence criterion for right - angled triangles states that if a leg and an acute angle of one right - angled triangle are equal to the corresponding leg and acute angle of another right - angled triangle, then the two triangles are congruent. Here, we have a leg (marked equal) and an acute angle ($20^{\circ}$) equal in both right - angled triangles. So, the triangles are congruent by LA.

Answer:

The triangles are congruent by LA.