Question

437 5

53
3
Select the two pairs of figures that are similar.
Angle measures are rounded to the nearest integer.
53
10
4
4
4
10
T
CLEAR CHECK
8

Answer 1

In the given options, the pair of similar figures is in option (a) with triangles having side ratios of 1:2, indicating proportionality and similarity. The rectangles in options (b) and (c) are not similar.

The pairs of figures that are similar have corresponding sides that are proportional. Let's analyze each pair:

a. Triangles:

- Triangle 1: Base-3, Height-4, Hypotenuse-5

- Triangle 2: Base-6, Height-8, Hypotenuse-10

Check if the ratios of corresponding sides are equal:

-
`\( (Base_1)/(Base_2) = (3)/(6) = (1)/(2) \)`

-
`\( (Height_1)/(Height_2) = (4)/(8) = (1)/(2) \)`

-
`\( (Hypotenuse_1)/(Hypotenuse_2) = (5)/(10) = (1)/(2) \)`

Since all ratios are equal, the triangles are similar.

b. Rectangles:

- Figure 1: Length=10, Breadth=4

- Figure 2: Length=4, Breadth=4

Check if the ratios of corresponding sides are equal:

-
`\( (Length_1)/(Length_2) = (10)/(4) \\eq (Breadth_1)/(Breadth_2) = (4)/(4) \)`

The rectangles are not similar.

c. Rectangles:

- Figure 1: Length=2, Breadth=4

- Figure 2: Length=8, Breadth=2

Check if the ratios of corresponding sides are equal:

-
`\( (Length_1)/(Length_2) = (2)/(8) \\eq (Breadth_1)/(Breadth_2) = (4)/(2) \)`

The rectangles are not similar.

Therefore, the pair of similar figures is option (a) with similar triangles.