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olga2289 [7]
2 years ago
6

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Mathematics
1 answer:
luda_lava [24]2 years ago
4 0

Both triangles are congruent by either ASA or AAS Congruence Theorem. hence, the right answer is A: Yes, they are congruent by either ASA or AAS.

<h3>What is ASA Congruence Theorem?</h3>

The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.

The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.

Triangle LMQ is shown in the figure attached below.

Thus, Proving

Triangle MNL ≅ triangle QNL (ASA)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <MLN and <QLN

Also, they have a common side: side LN (included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

Triangle MNL ≅ triangle QNL ( by AAS)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <NML and <NQL

Also, they have a common side: side LN (non-included side).

Thus, Triangle MNL and triangle QNL are congruent by ASA.

Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.

Learn more about the ASA and AAS Congruence Theorem on:

brainly.com/question/2102943

#SPJ1

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Oliver and Lenny started hiking a hill simultaneously from the bottom to the top. Oliver hiked at a speed of 5 km/h during the f
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Answer:

<u>Oliver and Lenny reached the top of the hill at the same time</u>

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Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Oliver's speed = 5 km/h during the first half, then decreased his speed to 4 km/h during the second half.

Lenny's speed = 4 km/h during the first half, then increased his speed to 5 km/h in the second half.

2. Who reached the top of the hill first? What is the proportion of time he spent hiking to that of his friend?

Let's assume the distance from the bottom to the top of the hill is 10 kilometers for calculating the time it will take Oliver and Lenny to reach the top of the hill:

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<u>Oliver and Lenny reached the top of the hill at the same time</u>

<u>The proportion of time Oliver spent hiking to that of Lenny is 1:1</u>

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Write the equation of the line parallel to the line and passing through the point.
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Answer:

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Using the point (8,1) we can form our own equation.

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All we have to do is find C in order to form the equation <em>y</em><em>=</em><em>mx</em><em>+</em><em>c</em>

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