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 that 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 three main criteria for triangle similarity are: 1. AA (Angle-Angle) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SAS (Side-Angle-Side) 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. SSS (Side-Side-Side) Criterion: If the corresponding sides of two triangles are in proportion, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does the 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 two triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What does the SAS 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 two triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does the SSS criterion state?

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

If two triangles have angles measuring 30°, 60°, and 90°, are they similar?

Back

Yes, they are similar because they have the same angle measures.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

The lengths of the corresponding sides of triangle ABC and triangle DEF are in proportion.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

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

Front

How do you find the missing length in similar triangles?

Back

To find the missing length in similar triangles, set up a proportion using the lengths of the corresponding sides and solve for the unknown length.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle XYZ is similar to triangle PQR and the length of XY is 10 cm and PQ is 5 cm, what is the ratio of their sides?

Back

The ratio of their sides is 10:5 or 2:1.

Tags

CCSS.HSG.SRT.A.2