Question

What additional information is needed to prove triangle LMN is congruent to triangle KMN using the HL theorem?

Answer 1

leg MN of both triangle is equal.

Step-by-step explanation

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called 'legs', or 'base' and 'height'.

It means we have two right-angled triangles with

1. the same length of hypotenuse
2. the same length for one of the other two legs

Since ∠ LMN and ∠KMN are right angle , the hypotenuse LN and and one leg LN of one right-angled triangle LMN are equal to the corresponding hypotenuse KN and leg MN of another right-angled triangle MKN, hence the two triangles are congruent.

Answer 2

∠LMN is a right angle

Explanation:

If we want to prove that two right triangles are congruent by knowing that the corresponding hypotenuses and one leg are congruent, we begin as follows:

• Since two legs are congruent and we know this by the hash marks, then the triangle ΔLKN is isosceles.
• By definition LN ≅ NK

• If ∠LMN is a right angle, then MN is the altitude of triangle ΔLKN
• Also MN is the bisector of LK, so KM ≅ ML
• So we have two right triangles ΔLMN and ΔKM having the same lengths of corresponding sides

• In conclusion, ΔLMN ≅ ΔKMN