To find: The scalar factor of the similarity of the given
Answer to Problem 9WE
The scalar factor of the similarity of the given triangles is
Explanation of Solution
Given information:
AB | BC | AC | TR | RI | TI |
6 | 8 | 10 | 20 | 25 | 15 |
SSS similarity theorem: If the sides of two triangles are in proportion, then the triangles are similar.
Scalar factor: If the two
Now consider one triangle has vertices A,B, and C and another triangle has vertices T, R, and I.
AB | BC | AC | TR | RI | TI |
6 | 8 | 10 | 20 | 25 | 15 |
Now,
Compare the longest sides,
Compare the shortest sides,
Compare the remaining sides,
Therefore,
All the corresponding sides of two triangles are in proportion, therefore the triangles are similar.
And as the scalar factor is the ratio of the length of two corresponding sides.
Therefore,
Scalar factor=
Hence, the given triangles are similar by SSS similarity theorem and the scalar factor of the similarity of the given triangles is
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