Question

question 6 of 20 (1 point) | question attempt: 1 of unlimited

can the hl congruence property be used?

(a) two right triangles with legs 21 km, hypotenuses 35 km
options: yes, no (selected no)

(b) two right triangles with marked legs
options: yes, no (selected no)

(c) two triangles with marked sides and an angle
options: yes, no

(d) a rectangle with a diagonal, right angles, marked sides
options: yes, no

try again

Explanation:

Part 1 (First pair of triangles)

The HL (Hypotenuse - Leg) Congruence Property applies to right - angled triangles. For two right - angled triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of the other triangle, then the triangles are congruent. In the first pair of triangles, both are right - angled, they have the same hypotenuse (35 km) and the same leg (21 km). So, the HL Congruence Property can be used.

The HL Congruence Property is for right - angled triangles. The second pair of triangles: one has a right angle, but we need to check the hypotenuse and leg. The marked sides are not the hypotenuse - leg combination as required by HL. Also, the triangles do not have the correct corresponding hypotenuse and leg equal in the way HL requires. So, HL cannot be used.

The HL Congruence Property is specific to right - angled triangles. The third pair of triangles (c) are not right - angled triangles. So, the HL Congruence Property, which is applicable only to right - angled triangles, cannot be used here.

Answer:

Yes

Part 2 (Second pair of triangles)