Question

how are the triangles congruent?

sas
sss
aas
hl

Explanation:

Step1: Recall congruence criteria

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• HL (Hypotenuse - Leg): In right - angled triangles, the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle.

Step2: Analyze the given triangles

• The two triangles formed by the altitude in the isosceles triangle are right - angled triangles (the altitude is perpendicular to the base, so the angle is \(90^{\circ}\)).
• The hypotenuse of each right - angled triangle is the equal sides of the isosceles triangle (marked with two tick marks).
• The leg is the common altitude (the same line segment for both triangles).

Answer:

HL