Question

1. to use the hl theorem to prove two triangles are congruent, the triangles must be right triangles. which other conditions must also be met?

the triangles have congruent hypotenuses and two pairs of congruent legs.
the triangles have two pairs of congruent legs.
the triangles have congruent hypotenuses.
the triangles have congruent hypotenuses and one pair of congruent legs

Explanation:

The HL (Hypotenuse - Leg) Theorem specifically states that for two right - angled triangles, if the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.

• Option 1: Having two pairs of congruent legs would be the SAS (Side - Angle - Side) or LL (Leg - Leg) (for right - triangles) congruence, not HL.
• Option 2: Two pairs of congruent legs is again related to LL (for right - triangles) or SAS (in general triangle congruence, if the included angle is right - angle).
• Option 3: Just congruent hypotenuses is not enough. We need a leg as well.
• Option 4: This matches the HL (Hypotenuse - Leg) Theorem.

Answer:

The triangles have congruent hypotenuses and one pair of congruent legs.