Respuesta :
Answer:
Looking at both triangles, angle P in triangle PQR = 38 degrees. Angle N in triangle LMN = 38 degrees. Both angles are equal.
Side PQ in triangle PQR = 16
Side MN in triangle LMN = 8
Therefore,
PQ/MN = 16/8 = 2
Side PR in triangle PQR = 14
Side LN in triangle LMN = 7
Therefore,
PR/LN = 14/7 = 2
Therefore, triangle PQR is similar to
triangle LMN because
1) the length of PQ is proportional to the length of MN.
2) the length of PR is proportional to the length of LN
3) angle P = angle N
4) Therefore, QR is also proportional to ML
Therefore,
PQ/MN = PR/LN = QR/ML = 2
Step-by-step explanation:
The pair of the first two triangles are not similar triangles, while the pair of the next two triangles are similar triangles.
What are similar triangles?
If the respective angles are congruent and the corresponding sides are proportional, two triangles are said to be similar. To put it another way, comparable triangles are similar in shape but not necessarily in size. In addition, the triangles are congruent if their corresponding sides are of identical length.
As it we know that for the two triangles to be similar triangles, the ratio of their corresponding sides should be the same.
A.) In the first pair of triangles,
For the first pair of triangles to be similar,
[tex]\dfrac{US}{UD}=\dfrac{UT}{UE}=\dfrac{ST}{DE}[/tex]
The above ratio should be similar, but since we can see that the ratio,
[tex]\dfrac{US}{UD}\neq \dfrac{UT}{UE}[/tex]
[tex]\dfrac{39}{16}\neq \dfrac{40}{16}[/tex]
As we can see that the ratio of the sides of the triangle is not the same therefore, the two of the given triangles are not similar triangles.
B.) In the second pair of triangles,
For the second pair of triangles to be similar,
[tex]\dfrac{AB}{HG}=\dfrac{BC}{GF}=\dfrac{CA}{FH}[/tex]
The above ratio should be similar, and as we can see that the ratio,
[tex]\dfrac{72}{12}=\dfrac{48}{8}=\dfrac{84}{14} =6[/tex]
As we can see that the ratio of the sides of the triangle is the same therefore, the two of the given triangles are similar triangles.
Learn more about Similar Triangles:
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