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. ha
b. sss
c. sas
d. aas
e. hl
f. la

Explanation:

• HA (Hypotenuse - Angle): Not applicable as there is no information about a non - right angle being congruent in the given diagram.
• SSS (Side - Side - Side): The diagram shows two right - angled triangles. For right - angled triangles, SSS is not the most appropriate congruence criterion when we already have right angles and some side - side relationships.
• SAS (Side - Angle - Side): The right angles (\(\angle A=\angle D = 90^{\circ}\)) are the included angles. We can observe that two sides (one leg and the hypotenuse) are congruent.
• AAS (Angle - Angle - Side): There is no second non - right angle information given in the diagram to apply AAS.
• HL (Hypotenuse - Leg): In right - angled triangles (\(\triangle ABC\) and \(\triangle DEF\) with \(\angle A=\angle D = 90^{\circ}\)), if the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the triangles are congruent.
• LA (Leg - Angle): No non - right angle information is given in the diagram to apply LA.

Answer:

C. SAS, E. HL