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4 years ago

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

Mathematics

2 answers:

Alexxx [7]4 years ago

6 0

<h3>Answer</h3>

leg MN of both triangle is equal.

<h3>Step-by-step explanation</h3>

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

the same length of hypotenuse
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.

IgorC [24]4 years ago

3 0

<h2>Answer:</h2>

∠LMN is a right angle

<h2>Step-by-step explanation:</h2>

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

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Read 2 more answers

. Find each of the following probabilities for a normal distribution. a. p(21.80 , z , 0.20) b. p(20.40 , z , 1.40) c. p(0.25 ,

Ulleksa [173]

Correct question is;

A. p(-1.80 < z < 0.20 )

B. p(-0.4 < z < 1.4)

C. p(0.25 < z < 1.25)

D. p(-0.9 < z < -0.6)

Answer:

A) p(-1.80 < z < 0.20) = 0.54333

B) p(-0.4 < z < 1.4) = 0.57466

C) p(0.25 < z < 1.25) = 0.29564

D) p(-0.9 < z < -0.6) = 0.90981

Step-by-step explanation:

A) p(-1.80 < z < 0.20 )

This gives us;

P(z < 0.2) - P(z < -1.8)

From z-distribution tables;

P(z > 0.2) = 0.57926

And P(z < -1.8) = 0.03593

Thus;

p(-1.80 < z < 0.20) = 0.57926 - 0.03593 p(-1.80 < z < 0.20) = 0.54333

B) p(-0.4 < z < 1.4)

This gives us;

P(z < 1.4) - P(z < -0.4)

From z-distribution table, we have;

P(z > 1.4) = 0.91924

P(z < -0.4) = 0.34458

Thus;

p(-0.4 < z < 1.4) = 0.91924 - 0.34458

p(-0.4 < z < 1.4) = 0.57466

C) p(0.25 < z < 1.25)

From z-distribution table, we have;

P(z < 0.25) = 0.59871

P(z > 1.25) = 0.10565

Now, to solve this;

p(0.25 < z < 1.25) = 1 - (P(z < 0.25) + P(z > 1.25))

This gives;

p(0.25 < z < 1.25) = 1 - (0.59871 + 0.10565)

p(0.25 < z < 1.25) = 0.29564

D) p(-0.9 < z < -0.6)

From z-distribution table, we have;

P(z < -0.9) = 0.18406

P(z > -0.6) = 0.72575

Thus;

p(-0.9 < z < -0.6) = 0.18406 + 0.72575

p(-0.9 < z < -0.6) = 0.90981

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