Question

determining when to apply the hl congruence property
each pair of triangles, determine whether the hypotenuse-leg (hl) congruence property can be used to prove that the triangles are congruent.
if necessary, you may learn what the markings on a figure indicate.
(a)
triangle with right angle, one leg 9 km, hypotenuse 15 km.
triangle with right angle, one leg 9 km, hypotenuse 15 km.
can the hl congruence property be used?
options: yes, no
(b)
right triangle with one leg marked congruent.
right triangle with one leg marked congruent.
can the hl congruence property be used?
options: yes, no
(c)
triangle with two sides marked congruent and an angle.
triangle with two sides marked congruent and an angle.
can the hl congruence?
options: yes, no
(d)
rectangle with a diagonal, sides marked congruent, right angles.
can the hl congruence?
options: yes, no

Explanation:

Part (a)

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent. In part (a), both triangles are right - angled. One leg of each triangle is \(9\) km and the hypotenuse of each triangle is \(15\) km. So, the hypotenuse and one leg of the first right triangle are congruent to the hypotenuse and one leg of the second right triangle. Thus, the HL Congruence property can be used.

For the HL Congruence Theorem, we need a hypotenuse and a leg to be congruent between two right triangles. In part (b), the marked sides are legs, but we don't know about the hypotenuses. The HL theorem requires the hypotenuse to be involved in the congruence. Since we only have information about the legs (and not the hypotenuses), we cannot apply the HL Congruence property.

The HL Congruence Theorem is applicable only to right - angled triangles. The triangles in part (c) are not right - angled (there are no right - angle markings). So, the HL Congruence property, which is specific to right triangles, cannot be used here.

Answer:

Yes

Part (b)