Question

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

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

Explanation:

• The LL (Leg - Leg) theorem for right - angled triangles states that 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.
• In the 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 triangles are congruent. In a right - angled triangle, the right angle is the included angle between the two legs. So, LL is a special case of SAS (where the included angle is \(90^{\circ}\)).
• Also, in a right - angled triangle, if we know two legs (LL), we can use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(a\) and \(b\) are legs and \(c\) is the hypotenuse) to find the hypotenuse. So, if two legs of two right - angled triangles are equal, all three sides (by Pythagorean theorem) are equal. And the SSS (Side - Side - Side) postulate states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. So, LL is also a special case of SSS for right - angled triangles.

Answer:

D. SAS postulate or SSS postulate