Chapter 10: Q61. (page 660)

Find the missing measures for the pair of similar triangles if $Δ A B C ~ Δ D E F$ .
$a = 3, b = 4, c = 5, d = 4.5$

Short Answer

Expert verified

The missing measures for the pairs of similar triangles are $e = 6$ and $f = 7.5$ .

Step by step solution

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.

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

The rough sketch of the triangles $Δ A B C$ and $Δ D E F$ are:

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

As, the triangles $Δ A B C$ and $Δ D E F$ are similar, therefore the measures of their corresponding sides are proportional.

That implies,

$\frac{B C}{E F} = \frac{A C}{D F} = \frac{A B}{D E}$

Therefore, it can be said that:

$\frac{B C}{E F} = \frac{A C}{D F} \frac{a}{d} = \frac{b}{e} \frac{3}{4.5} = \frac{4}{e} 3 e = 18 e = \frac{18}{3} e = 6$

$\frac{A C}{D F} = \frac{A B}{D E} \frac{b}{e} = \frac{c}{f} \frac{4}{6} = \frac{5}{f} 4 f = 30 f = \frac{30}{4} f = 7.5$

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

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Find the missing measures for the pair of similar triangles if $Δ A B C ~ Δ D E F$ .
$a = 3, b = 4, c = 5, d = 4.5$

Short Answer

Step by step solution

Step 1. Write the definition of similar triangles.

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

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

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Find the missing measures for the pair of similar triangles if ΔABC~ΔDEF.a=3,b=4,c=5,d=4.5

Short Answer

Step by step solution

Step 1. Write the definition of similar triangles.

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Probability and Statistics

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the missing measures for the pair of similar triangles if $Δ A B C ~ Δ D E F$ .
$a = 3, b = 4, c = 5, d = 4.5$