Question

question 5 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why \\( \triangle a b c \cong \triangle d e f \\)?
check all that apply.
a. sss
b. la
c. aas
d. ha
e. sas
f. hl

Explanation:

• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. In right - angled triangles (as shown in the diagram), if the hypotenuse and two legs (which are sides) are equal. Here, we can assume the equal markings on the sides correspond to equal lengths.
• HL (Hypotenuse - Leg): For right - angled triangles, if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, the triangles are congruent. The diagram shows right - angled triangles (\(\angle A=\angle D = 90^{\circ}\)) and the markings on the hypotenuse and one leg (from the equal side markings) imply HL can be used.

Answer:

A. SSS, F. HL