Question

question 9 of 10
the ll theorem is a special case of the

a. sas postulate or asa postulate
b. sas postulate or sss postulate
c. aas theorem or sss postulate
d. aas theorem or asa postulate

Explanation:

• LL (Leg - Leg) theorem: In right - angled triangles, if the two legs of one right - angled triangle are equal to the two legs of another right - angled triangle, the two right - angled triangles are congruent.
• SAS (Side - Angle - Side) postulate: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent. In a right - angled triangle, the right angle is the included angle between the two legs. So, when we use the LL theorem (two legs are equal), we can also consider it as a SAS case (two sides (legs) and the included right - angle).
• ASA (Angle - Side - Angle) postulate: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the two triangles are congruent. In right - angled triangles, we know that the right angles are equal. If we have two right - angled triangles with two legs (sides) equal, we can also think of it in terms of ASA. Let the right angles be one pair of equal angles. The legs can be considered as the included side between the right angle and the other acute angles (since in a right - angled triangle, \(\angle A+\angle B = 90^{\circ}\) for non - right angles \(A\) and \(B\)). If the legs (sides) are equal, and the right angles are equal, we can use the ASA concept (by considering the relationship between angles and sides in right - angled triangles).

Answer:

A. SAS postulate or ASA postulate