Question

Triangle JKL is dilated from the origin at a scale factor of 10 to create triangle J'K'L'. Select the option that completes the statement: The triangles are ________ because their corresponding sides are ________ and their corresponding angles are ________.

1) Congruent; congruent; proportional
2) Similar; congruent; proportional
3) Congruent; similar; similar
4) Similar; proportional; congruent

Answer 1

The correct description is that Triangle JKL and Triangle J'K'L' are similar; their corresponding sides are proportional and their corresponding angles are congruent due to a dilation with a scale factor of 10 from the origin.

Step-by-step explanation:

The statement that completes the description of the relationship between Triangle JKL and its dilation Triangle J'K'L' is: The triangles are similar because their corresponding sides are proportional and their corresponding angles are congruent. When a triangle is dilated from a point (in this case, the origin) with a scale factor (such as 10), the new triangle maintains the same shape but with an altered size. The angles remain the same, which is why they are congruent, and the sides are multiplied by the scale factor, hence they are proportional to the corresponding sides of the original triangle.