Question

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

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

Explanation:

• The LL (Leg - Leg) theorem is used for right - angled triangles. In a right - angled triangle, if the two legs of one right - angled triangle are equal to the two legs of another right - angled triangle, then the two right - angled triangles are congruent.
• The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. In a right - angled triangle, the right angle is the included angle between the two legs. So, LL theorem is a special case of the SAS postulate (where the included angle is \(90^{\circ}\)).
• The ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent. In a right - angled triangle, if we know the two legs (sides) and the right angle (angle), we can also consider it in the context of ASA (since we know two angles: the right angle and the fact that in right - angled triangles, if the legs are equal, the other two non - right angles are also equal due to trigonometric ratios and triangle angle sum property (\(180-(90 + \theta_1)=180-(90+\theta_2)\) implies \(\theta_1=\theta_2\) when the legs are equal), and the included side (one of the legs)).

Answer:

B. SAS postulate or ASA postulate