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Chapter 10: Q61. (page 660)

Find the missing measures for the pair of similar triangles if 螖ABC~螖DEF.

a=3,b=4,c=5,d=4.5

Short Answer

Expert verified

The missing measures for the pairs of similar triangles aree=6and f=7.5.

Step by step solution

01

Step 1. Write the definition of similar triangles.

The two triangles are said to be similar if the measures of the corresponding angles are equal and if the two triangles are similar then the measures of their corresponding sides are proportional.

02

Step 2. Draw the rough sketch of the triangles ΔABC and ΔDEF.

The rough sketch of the triangles螖ABC and螖DEF are:

03

Step 3. Find the missing measures for the pair of similar triangles if ΔABC~ΔDEF.

As, the triangles螖ABC and螖DEF are similar, therefore the measures of their corresponding sides are proportional.

That implies,

BCEF=ACDF=ABDE

Therefore, it can be said that:

BCEF=ACDFad=be34.5=4e3e=18e=183e=6

ACDF=ABDEbe=cf46=5f4f=30f=304f=7.5

Therefore, the missing measures for the pairs of similar triangles aree=6 and f=7.5.

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