Question

question 9 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 x y z \\)?
check all that apply.
\\( \square \\) a. hl
\\( \square \\) b. sss
\\( \square \\) c. ll
\\( \square \\) d. sas
\\( \square \\) e. asa
\\( \square \\) f. la

Explanation:

Step1: Analyze HL (Hypotenuse - Leg)

Both triangles are right - angled. If the hypotenuse and one leg of a right - triangle are equal to the hypotenuse and one leg of another right - triangle, the triangles are congruent. Here, assume the non - marked sides (hypotenuses) are equal (since other corresponding sides and angles are marked as equal in the right - triangle context).

Step2: Analyze LL (Leg - Leg)

For right - triangles, if two legs of one right - triangle are equal to two legs of another right - triangle, the triangles are congruent. The marked equal sides (legs) in the right - triangles \( \triangle ABC\) and \( \triangle XYZ\) satisfy this.

Step3: Analyze SAS (Side - Angle - Side)

There is a pair of equal sides (legs), an equal included right - angle (or the marked equal acute angle can also be considered in the non - right - angle part of the SAS logic if we re - frame the sides and included angle correctly as per the diagram's marked equal elements), and another pair of equal sides (legs).

Answer:

A. HL, C. LL, D. SAS