Question

quiz pt.2 - similar triangles
36
show your work here
the two triangles are similar. the scale factor from the top triangle to the bottom triangle is \\(\frac{2}{3}\\).
the two triangles are similar. the scale factor from the top triangle to the bottom triangle is \\(\frac{3}{2}\\).
the two triangles are similar. the scale factor from the top triangle to the bottom triangle is \\(\frac{1}{3}\\).
the two triangles are similar. the scale factor from the top triangle to the bottom triangle is \\(\frac{1}{4}\\).
the triangles are not similar

Explanation:

Step1: Recall Similar Triangles

Similar triangles have proportional sides. Scale factor is ratio of corresponding sides (bottom to top or top to bottom). Wait, the diagram: top triangle and bottom? Wait, maybe the top triangle's side and bottom's. Wait, the bottom base is 36, maybe top base? Wait, maybe the left side: top triangle's side is, say, 24? Wait, the left side has "24" (maybe typo as "49"? No, maybe 24). Wait, if top triangle has a side, bottom has 36? Wait, no, maybe the left side: top is 24, bottom is 36? Wait, scale factor from top to bottom: bottom/top = 36/24 = 3/2? Wait, no, the options: one is 3/2? Wait, the second option: "the scale factor from the top triangle to the bottom triangle is 3/2". Wait, let's check: if top triangle's side is 24, bottom is 36, then 36/24 = 3/2. So scale factor from top to bottom is 3/2 (since bottom is larger, scale factor >1). So the correct option is the second one.

Step2: Verify Scale Factor

Scale factor from top to bottom: ratio of bottom side to top side. If top side is 24, bottom is 36, then \( \frac{36}{24} = \frac{3}{2} \). So the scale factor is \( \frac{3}{2} \), matching the second option.

Answer:

The two triangles are similar. The scale factor from the top triangle to the bottom triangle is \( \frac{3}{2} \) (the second option, assuming the left side of top is 24 and bottom is 36, or corresponding sides give 36/24 = 3/2).