Question

1. what property could you use to show that these two triangles are congruent?

hl
sss
asa
sas

Explanation:

Step1: Recall Congruence Properties

• HL (Hypotenuse - Leg): Applies to right - angled triangles. There is no indication that these are right - angled triangles.
• SSS (Side - Side - Side): Requires all three sides of one triangle to be equal to the corresponding sides of the other triangle. There is no information about all three sides.
• ASA (Angle - Side - Angle): Requires two angles and the included side of one triangle to be equal to the corresponding two angles and included side of the other triangle.
• SAS (Side - Angle - Side): Requires two sides and the included angle. But here we have two angles and a side (not the included side for SAS).

From the figure, we can see that two angles and a non - included side (but in the case of triangles, when two angles are equal, the third angle is also equal by the angle - sum property of triangles (\(180^{\circ}\) in a triangle). So, if two angles and a side (which is not included between the two angles in one triangle but in the other triangle, due to angle - sum property, it is equivalent to ASA) are equal.

Answer:

ASA