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 does AA Similarity stand for?

Back

AA Similarity stands for 'Angle-Angle Similarity'. It 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.B.5

Front

How can you determine if two triangles are similar?

Back

Two triangles can be determined to be similar if they satisfy one of the following conditions: 1) AA (Angle-Angle) similarity, 2) SSS (Side-Side-Side) similarity, or 3) SAS (Side-Angle-Side) similarity.

Tags

CCSS.HSG.SRT.A.2

Front

What is the SSS Similarity Criterion?

Back

The SSS (Side-Side-Side) Similarity 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 is the SAS Similarity Criterion?

Back

The SAS (Side-Angle-Side) Similarity Criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF has sides of lengths 6, 8, and 10, are the triangles similar?

Back

Yes, triangle ABC and triangle DEF are similar because their corresponding sides are in proportion (3:6, 4:8, 5:10).

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 sides.

Front

If triangle ABC is similar to triangle DEF and the length of side AB is 5 cm and side DE is 10 cm, what is the ratio of their sides?

Back

The ratio of the sides of triangle ABC to triangle DEF is 5:10, which simplifies to 1:2.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of corresponding sides in similar triangles?

Back

In similar triangles, corresponding sides are proportional, meaning the ratio of the lengths of any two corresponding sides is the same for all pairs of corresponding sides.

Tags

CCSS.HSG.SRT.A.2