Let's analyze the given statement to confirm whether it is true or false.
When we talk about similar triangles, we refer to triangles that have the same shape but not necessarily the same size. This means that corresponding angles of the triangles are equal, and the corresponding sides are in proportion.
Now, let's break down the concept of similar triangles and their properties:
1. Corresponding Angles are Equal: In similar triangles, every pair of corresponding angles is the same. That means if two triangles are similar, then the angles, say ∠A in triangle 1 and ∠A' in triangle 2, are equal.
2. Corresponding Sides are Proportional: For triangles to be similar, the ratio of the lengths of corresponding sides must be equal. This means if triangle 1 has sides a, b, and c, and triangle 2 has sides a', b', and c', then the following ratios must be true:
[tex]\[
\frac{a}{a'} = \frac{b}{b'} = \frac{c}{c'}
\][/tex]
Given these properties, when triangles are similar, the ratios of all three pairs of corresponding sides across the triangles are equal, indicating proportionality.
Therefore, the statement "With similar triangles, the ratios of all three pairs of corresponding sides are equal." is:
A. True
The concept of proportionality of corresponding sides confirms that for similar triangles, the ratio of one pair of corresponding sides will be the same for all pairs. Thus, the original statement is indeed true.
