ΔABC is dilated from the origin at a scale factor of 3 to create ΔA′B′C′. Select the option that completes the statement: The triangles' corresponding angles are ________, and thei... ΔABC is dilated from the origin at a scale factor of 3 to create ΔA′B′C′. Select the option that completes the statement: The triangles' corresponding angles are ________, and their corresponding sides are ________; therefore, the triangles are ________.
Understand the Problem
The question is asking to select the correct completion for a statement regarding the properties of triangles ΔABC and ΔA′B′C′ after dilation. It involves concepts of congruence, similarity, and proportionality of angles and sides of the triangles.
Answer
Congruent; proportional; similar
The triangles' corresponding angles are congruent, and their corresponding sides are proportional; therefore, the triangles are similar.
Answer for screen readers
The triangles' corresponding angles are congruent, and their corresponding sides are proportional; therefore, the triangles are similar.
More Information
When a triangle is dilated, its angles remain the same (congruent), whereas its sides are scaled by the factor of dilation, making them proportional; hence the triangles are similar by definition.
Tips
A common mistake is to think that since the triangles change in size, angles would also change, which is not the case with dilation.
Sources
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