Question

4 which of the following triangles could lie on the line graphed in question #2? a 21 44 b. 12 36 c. 20 30 d. 26 52

Explanation:

Step1: Check Proportions for Similar Triangles

For triangles to be similar, their corresponding sides must be in proportion (i.e., the ratios of corresponding sides are equal). Let's calculate the ratio of the two given sides for each triangle:

• Triangle A: Sides 21 and 44. Ratio = $\frac{21}{44} \approx 0.477$
• Triangle B: Sides 12 and 36. Ratio = $\frac{12}{36} = \frac{1}{3} \approx 0.333$
• Triangle C: Sides 20 and 30. Ratio = $\frac{20}{30} = \frac{2}{3} \approx 0.666$
• Triangle D: Sides 26 and 52. Ratio = $\frac{26}{52} = \frac{1}{2} = 0.5$

Wait, maybe the problem is about a line graph (probably a proportional relationship, like a graph of side lengths with a constant ratio). Let's re - evaluate. If we assume the line has a slope (ratio) that we need to match. Let's check the ratio of the two sides (let's say vertical to horizontal or vice - versa) for each triangle:

For Triangle D: $\frac{26}{52}=\frac{1}{2}$, Triangle A: $\frac{21}{44}\approx0.477$, Triangle B: $\frac{12}{36}=\frac{1}{3}$, Triangle C: $\frac{20}{30}=\frac{2}{3}$. If we consider that maybe the line has a ratio of 1:2 (since 26 and 52 have a ratio of 1:2), then Triangle D has sides in the ratio 1:2. Let's confirm: 262 = 52, so the two sides are in the ratio 1:2. For the other triangles: 212 = 42≠44, 123 = 36 (ratio 1:3), 201.5 = 30 (ratio 2:3). So Triangle D has sides with a ratio of 1:2, which is a constant proportion, so it could lie on a line graph representing proportional side lengths (similar triangles have proportional sides).

Step2: Confirm the Ratio

The key is that for similar triangles (or triangles that can lie on a proportional line graph), the ratio of corresponding sides must be constant. For Triangle D, the ratio of the two given sides is $\frac{26}{52}=\frac{1}{2}$, which is a constant ratio. For the other triangles, the ratios are different. So Triangle D (with sides 26 and 52) has sides in a constant proportion, so it could lie on the line graph.

Answer:

D. The triangle with sides 26 and 52