Similarity - SSS, SAS, AA

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side similarity, which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side similarity, which 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.

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle similarity, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

Not necessarily. To determine similarity, we need to check if the angles are also equal or if the sides are in proportion with a third triangle.

Front

What is the criterion for two triangles to be similar using SSS?

Back

The criterion for SSS similarity is that the ratios of the lengths of corresponding sides must be equal.

Front

Can two triangles be similar if only one pair of angles is equal?

Back

No, two triangles cannot be similar with only one pair of equal angles; at least two pairs of angles must be equal (AA criterion).

Front

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

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

Back

Yes, they are similar by SSS because the sides are in proportion (3:6, 4:8, 5:10).

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

Back

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