Which statement describes the relationship, if any, that exists between triangle KLM and triangle NPQ?
Triangle L K M. Side K L is 16, L M is 22, K M is 12. Triangle P N Q. Side P N is 8, N Q is 6, P Q is 11. Angles L and P are congruent, Q and M are congruent, K and N are congruent.
They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio Three-halves from Triangle K L M to triangle N P Q.
They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio StartFraction 2 Over 1 EndFraction from Triangle K L M to triangle N P Q.
They are not similar because their corresponding angles are not congruent.
They are not similar because their corresponding side lengths are not proportional.
Answers
Answer:
Option 2_They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio StartFraction 2 Over 1 EndFraction from Triangle K L M to triangle N P Q.
Step-by-step explanation:
Because,
For Similarity
The Ratio of the corresponding sides should be equal and in this case it is the same and the ratio is 2:1 and all the angles are congruent....
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They are similar because their corresponding angles are congruent and their corresponding side lengths are in the ratio Three-halves from Triangle KLM to triangle NPQ.
When two triangles are similar, their respective sides and angles must be in relation to one another and be congruent. Angles L and P, Q and M, and K and N are all declared to be congruent in the provided case. This satisfies one requirement for resemblance because the matching angles of the two triangles are congruent.
We need to examine the ratios of the respective sides to see if the two triangles are comparable based on the corresponding side lengths. The information provided indicates that side KL is 16, side LM is 22, and side KM is 12. Along the same lines, side PN is 8, side NQ is 6, and side PQ is 11.
We can split the length of each side of one triangle by the corresponding side of the other triangle to determine the ratio of the respective sides of the two triangles. For instance, by dividing 16 by 8, which yields 2, we can determine the proportion of side KL to side PN. To obtain the ratios, we can repeat the process for the other sets of matching sides:
KL/PN = 2
LM/NQ = 11/6
KM/PQ = 12/11
The respective edges of the two triangles are not proportionate to one another because not all of the ratios are equal. The right response is "They are not similar because their corresponding side lengths are not proportional" because we cannot infer that the two triangles are similar based on their corresponding side lengths.
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