Similar Triangles: Applying the formula

Examples with solutions for Similar Triangles: Applying the formula

Exercise #1

In the image there are a pair of similar triangles and a triangle that is not similar to the others.

Determine which are similar and calculate their similarity ratio.

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Step-by-Step Solution

Triangle a and triangle b are similar according to the S.S.S (side side side) theorem

And the relationship between the sides is identical:

GHDE=HIEF=GIDF \frac{GH}{DE}=\frac{HI}{EF}=\frac{GI}{DF}

96=31=62=3 \frac{9}{6}=\frac{3}{1}=\frac{6}{2}=3

That is, the ratio between them is 1:3.

Answer

a a and b b , similarity ratio of 3 3

Exercise #2

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

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Video Solution

Step-by-Step Solution

Triangle ABC is isosceles, therefore angle B is equal to angle C. We can calculate them since the sum of the angles of a triangle is 180:

18050=130 180-50=130

130:2=65 130:2=65

As the triangles are similar, DE is parallel to BC

Angles B and D are corresponding and, therefore, are equal.

B=D=65

Answer

65 65 °

Exercise #3

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.

Angle A is equal to 30°.

Calculate the size of angle E.

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Video Solution

Answer

75° 75\degree

Exercise #4

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.
Angle A is equal to 40°.

Calculate angle D.

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Video Solution

Answer

70° 70\degree

Exercise #5

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 60°.

Calculate angle E.

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Video Solution

Answer

60 60

Exercise #6

Triangle ADE is similar to equilateral triangle ABC.

Angle A is equal to 20°.

Calculate angle D.

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Video Solution

Answer

80 80

Exercise #7

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 35°.

What is the size of angle D?

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Video Solution

Answer

85 85 °

Exercise #8

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 60°.

Angle B is equal to 70°.

What is the size of angle F?

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Video Solution

Answer

50 50 °

Exercise #9

Triangle DEF is congruent to triangle ABC.

Angle D is equal to 45°.

Angle F is equal to 65°.

What is the size of angle B?

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Video Solution

Answer

70 70 °

Exercise #10

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 70°.

Angle C is equal to 55°.

What is the size of angle E?

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Video Solution

Answer

55 55 °

Exercise #11

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 75°.

What is the size of angle D?

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Video Solution

Answer

45 45 °