Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity include: 1) Angle-Angle (AA) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2) Side-Angle-Side (SAS) Criterion: If one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, the triangles are similar. 3) Side-Side-Side (SSS) Criterion: If the corresponding sides of two triangles are in proportion, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

Are triangles with angles 40°, 60°, and 80° similar to triangles with angles 40°, 50°, and 90°?

Back

No, because the angles do not match.

Tags

CCSS.HSG.SRT.A.2

Front

If two triangles have angles 40° and 60°, and another triangle has angles 60° and 40°, are they similar?

Back

Yes, they are similar because they have the same angles.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional to each other.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If Triangle A has sides of lengths 3, 4, and 5, and Triangle B has sides of lengths 6, 8, and 10, are they similar?

Back

Yes, they are similar because the sides are in proportion (1:2).

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

How do you find the height of a tree using similar triangles?

Back

You can use the ratio of the height of the tree to the length of its shadow and compare it to the ratio of a known height and shadow length of another object.

Tags

CCSS.HSG.SRT.B.5

Front

If Triangle A is similar to Triangle B and the length of a side in Triangle A is 12 and the corresponding side in Triangle B is 18, what is the scale factor?

Back

The scale factor is 18/12 = 1.5.

Tags

CCSS.7.G.A.1

Front

What is the AA criterion for triangle similarity?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

The areas of similar triangles are in the ratio of the square of their corresponding side lengths.