Are the triangles in the given figure similar? If yes, by which test ?
Practice Set 1.3 | Q 2 | Page 21
Are the triangles in the given figure similar? If yes, by which test ?
Given:
PQ = 6
PR = 10
QR = 8
LM = 3
LN = 5
MN = 4
Now,
\[\frac{PQ}{LM} = \frac{6}{3} = 2, \]
\[\frac{QR}{MN} = \frac{8}{4} = 2, \]
\[\frac{RP}{NL} = \frac{10}{5} = 2\]
\[\therefore \frac{PQ}{LM} = \frac{QR}{MN} = \frac{RP}{NL}\]
By SSS test of similarity
△PQR ∼ △LMN
Answer;-
The given triangles are △PQR and △LMN.
To check if these triangles are similar or not, we need to check if their corresponding angles are equal and their corresponding sides are in proportion.
Given that PQ = 6, PR = 10, QR = 8, LM = 3, LN = 5, MN = 4.
Comparing the corresponding sides of the two triangles, we get:
PQ/LM = 6/3 = 2
QR/MN = 8/4 = 2
RP/NL = 10/5 = 2
Since the ratios of the corresponding sides are equal, we can say that the corresponding sides of the two triangles are in proportion.
Now, we need to check if the corresponding angles are equal or not.
Therefore, we can say that the two triangles are similar by SSS test of similarity.
Chapter 1. Similarity- Practice Set 1.3 – Page 21
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