Properties of Similar Triangles

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What is the definition of similar triangles?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

What is the symbol used to denote similarity between triangles?

The symbol '~' is used to denote similarity between triangles.

If two triangles are similar, what can be said about their angles?

All corresponding angles of similar triangles are equal.

How do the sides of similar triangles compare to each other?

The lengths of corresponding sides of similar triangles are in proportion.

What is the AA criterion for triangle similarity?

Two triangles are similar if two pairs of corresponding angles are equal.

What is the SSS criterion for triangle similarity?

Two triangles are similar if all three pairs of corresponding sides are in proportion.

What is the SAS criterion for triangle similarity?

Two triangles are similar if two pairs of sides are in proportion and the included angle is equal.

How do you find the scale factor between two similar triangles?

The scale factor is the ratio of any pair of corresponding sides of the similar triangles.

Can right triangles be similar to other right triangles?

Yes, right triangles can be similar if they meet the angle-similarity or side-similarity criteria.

How does similarity of triangles relate to real-world applications?

Similar triangles can be used in real-world applications such as determining heights of tall objects using indirect measurements.

If triangle ABC ~ triangle DEF and AB = 4, AC = 6, DE = 8, what is DF?

DF = 12, using the proportion (AB/DE = AC/DF).

What is a practical method to test triangle similarity in construction?

Builders often use a ruler and a protractor to check angle measures and side lengths for similarity.

If the ratio of the perimeters of two similar triangles is 1:3, what is the ratio of their areas?

The ratio of their areas is 1:9 because the area ratio is the square of the perimeter ratio.

Can two equilateral triangles be considered similar? Why?

Yes, all equilateral triangles are similar to each other because they have equal angles and proportional sides.

What role does the centroid play in similar triangles?

In similar triangles, the centroid divides each median in a ratio of 2:1, regardless of the size of the triangles.




Test Your Knowledge

Select the correct option


1. What is the definition of similar triangles?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Two triangles are similar if they have two equal sides.

Two triangles are similar if their perimeters are equal.

Two triangles are similar if they have one right angle.

2. What is the symbol used to denote similarity between triangles?

The symbol '#' is used to denote similarity between triangles.

The symbol '@' is used to denote similarity between triangles.

The symbol '~' is used to denote similarity between triangles.

The symbol '&' is used to denote similarity between triangles.

3. If two triangles are similar, what can be said about their angles?

All corresponding angles of similar triangles are equal.

Only one pair of corresponding angles are equal.

Similar triangles have no angles in common.

All angles are complementary.

4. If triangle ABC ~ triangle DEF and AB = 4, AC = 6, DE = 8, what is DF?

DF = 12, using the proportion (AB/DE = AC/DF).

DF = 9, tripling one side.

DF = 16, doubling AC.

DF = 10, remaining proportional.

5. What is the SSS criterion for triangle similarity?

Two triangles are similar if they have three equal angles.

Two triangles are similar if they have two equal angles.

Two triangles are similar if all three pairs of corresponding sides are in proportion.

Two triangles are similar if they have no equal sides.