Question

question 3 of 10
the ha theorem is a special case of the _.
a. sss postulate
b. sas postulate
c. asa postulate
d. aas theorem

Explanation:

• HA (Hypotenuse - Angle) theorem: In a right - triangle, if the hypotenuse and an acute angle of one right - triangle are congruent to the hypotenuse and an acute angle of another right - triangle, then the two right - triangles are congruent.
• AAS (Angle - Angle - Side) theorem: If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
• In right - triangles (where we use HA), we know that one of the angles is \(90^{\circ}\). So, when we have the hypotenuse (a side) and an acute angle (an angle), along with the right angle (\(90^{\circ}\) angle), it is equivalent to having two angles (the right angle and the given acute angle) and a side (the hypotenuse) which is the AAS (Angle - Angle - Side) case.

Answer:

D. AAS theorem