Triangle Similarity

Front

What is triangle similarity?

Back

Triangle similarity occurs when two triangles have the same shape but may differ in 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 determining if two triangles are similar?

Back

The criteria for triangle similarity include: Angle-Angle (AA) criterion, Side-Side-Side (SSS) similarity criterion, and Side-Angle-Side (SAS) similarity criterion.

Tags

CCSS.HSG.SRT.B.5

Front

What does the Angle-Angle (AA) criterion state?

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

What does the Side-Side-Side (SSS) similarity criterion state?

Back

The SSS criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does the Side-Angle-Side (SAS) similarity criterion state?

Back

The SAS criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

How can you determine if two triangles are similar using proportions?

Back

To determine if two triangles are similar using proportions, compare the lengths of corresponding sides. If the ratios of the lengths of the sides are equal, the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal, which helps establish the similarity of the triangles.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle A is similar to triangle B, what can be said about their corresponding sides?

Back

If triangle A is similar to triangle B, then the lengths of their corresponding sides are in proportion.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

Can two triangles be similar if they have different side lengths?

Back

Yes, two triangles can be similar even if they have different side lengths, as long as their corresponding angles are equal.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6