Question

which theorem or postulate could be used to prove the congruence of the pair of triangles?
o la
o hl
o ll
o ha

Explanation:

Step1: Recall triangle congruence theorems for right - triangles

For right - triangles, we have several congruence theorems:

• LA (Leg - Angle): One leg and an acute angle of one right - triangle are congruent to the corresponding leg and acute angle of another right - triangle.
• HL (Hypotenuse - Leg): The hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle.
• LL (Leg - Leg): Both legs of one right - triangle are congruent to both legs of another right - triangle.
• HA (Hypotenuse - Angle): The hypotenuse and an acute angle of one right - triangle are congruent to the hypotenuse and an acute angle of another right - triangle.

Step2: Analyze the given triangles

In the given figure, we can observe that the two right - triangles have their corresponding legs congruent. There is no information about the hypotenuse or angles (other than the right - angle which is common to both right - triangles).

Since we know that both legs of one right - triangle are congruent to both legs of the other right - triangle, we use the LL (Leg - Leg) congruence theorem for right - triangles.

Answer:

LL