Similar Triangles: Applying the formula

Question 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.

Question 2

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

Question 3

Triangle ADE is similar to equilateral triangle ABC.

Angle A is equal to 20°.

Calculate angle D.

Question 4

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 60°.

Calculate angle E.

Question 5

Triangle ADE is similar to triangle ABC.

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

Calculate angle D.

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.

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:

$\frac{GH}{DE}=\frac{HI}{EF}=\frac{GI}{DF}$

$\frac{9}{6}=\frac{3}{1}=\frac{6}{2}=3$

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

Answer

$a$ and $b$ , similarity ratio of $3$

Exercise #2

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

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:

$180-50=130$

$130:2=65$

As the triangles are similar, DE is parallel to BC

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

Answer

$70\degree$

Question 1

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.

Angle A is equal to 30°.

Calculate the size of angle E.

Question 2

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?

Question 3

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?

Question 4

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?

Question 5

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?

Exercise #6

Angle F is equal to 65°.

What is the size of angle B?

Exercise #11

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?

Video Solution

Answer

$70$ °