Question

question 1 of 10
based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why △abc≅△uvw?
check all that apply.
a. sas
b. la
c. asa
d. ll
e. aas
f. hl

Explanation:

• SAS (Side - Angle - Side): 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 right - angled triangles (as shown), if the legs (the two sides forming the right angle) are equal, we can use SAS. Here, assume \(AB = UV\), \(AC=UW\) and \(\angle A=\angle U = 90^{\circ}\) (the included angle between the two sides).
• LA (Leg - Angle): For right - angled triangles, if a leg and an acute angle of one right - angled triangle are equal to a leg and an acute angle of another right - angled triangle, the triangles are congruent.
• LL (Leg - Leg): 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 triangles are congruent. This is a special case of SAS for right - angled triangles.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent. In right - angled triangles, we know one angle is \(90^{\circ}\), and if another pair of angles and a non - hypotenuse side are equal.
• HL (Hypotenuse - Leg): For right - angled triangles, if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, the triangles are congruent.

Answer:

A. SAS, B. LA, D. LL, E. AAS, F. HL