Question

example 6
multiple - choice question
ex6: which congruency theorem can be used to prove that these triangles are congruent?
hl
sss
sas
asa
aas

Explanation:

Step1: Recall congruency theorems

• 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.
• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• 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.
• 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.

Step2: Analyze the given triangles

In the given figure, we have two triangles \(\triangle UV S\) and \(\triangle TVS\).
We can observe that \(UV = TV\) (given as marked equal), \(\angle UV S=\angle TVS\) (given as marked equal) and \(VS = VS\) (common side).
So, we have two sides and the included angle equal.

Answer:

SAS (Side - Angle - Side)