Question

Determine the missing side lengths and angles for the similar triangles in the picture below.

∠C =


∠F =



AB =


DF =

NO LINKS!

Answer 1

∡C=53°

∡F=102°

AB=11

DF=27

Explanation:

Similar triangles have the same shape but not necessarily the same size. If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Some of the properties of similar triangles:

• The ratio of any two corresponding sides of similar triangles is the same.
• The ratio of the areas of two similar triangles is the square of the ratio of any two corresponding sides.°Z
• The ratio of the perimeters of two similar triangles is the same as the ratio of any two corresponding sides.
• The heights and medians of similar triangles are proportional to the corresponding sides of the triangles.

For the question:

In ΔABC and ΔEFD

Since the respective corresponding angles are equal.

so,

∡A=∡E=25°

∡B=∡F=102°

∡C=∡D=53°

so, ΔABC
`\sim` ΔEFD

Again

Since their corresponding sides are proportional.

First, we need to find the ratio of their respective side:

DE: CA=63:14=9:2 when compared to big triangle to small triangle.

CA: DE=14:63=2:9 when compared to big triangle to small triangle.

AB=2/9*EF=2/9*49.5=11

DF=9/2*CB=9/2*6=27