Question

the table shows the side lengths for four right triangles. the graph shows the side lengths for a different right triangle. if all the triangles use the same units to measure their side lengths, which triangle in the table is similar to the triangle in the graph?
triangle | a | b | c | d
height | 4 | 2 | 3 | 4
base | 6 | 2 | 4 | 3

Explanation:

Step1: Find the ratio of the graph's triangle

The triangle in the graph has height \( 2 \) and base \( 3 \), so the ratio of height to base is \( \frac{2}{3} \).

Step2: Calculate ratios for each option

• Triangle A: Height \( 4 \), Base \( 6 \). Ratio: \( \frac{4}{6}=\frac{2}{3} \).
• Triangle B: Height \( 2 \), Base \( 2 \). Ratio: \( \frac{2}{2} = 1 \).
• Triangle C: Height \( 3 \), Base \( 4 \). Ratio: \( \frac{3}{4} \).
• Triangle D: Height \( 4 \), Base \( 3 \). Ratio: \( \frac{4}{3} \).

Answer:

A. Triangle A (Height = 4, Base = 6)