Similar Triangles (Part 1)

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may have different sizes; their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle; if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side; if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side; if the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

Are all angles in similar triangles congruent?

Back

True; all corresponding angles in similar triangles are congruent.

Front

If two triangles have one angle of 60 degrees and another angle of 30 degrees, are they similar?

Back

Yes, by AA, since two angles are equal.

Front

If triangle ABC is similar to triangle DEF, what can we say about their corresponding sides?

Back

The lengths of the corresponding sides are in proportion.

Front

Can two triangles be similar if they have no equal angles?

Back

No; for triangles to be similar, they must have at least two equal angles.

Front

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

Back

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

Front

What is the similarity statement for triangles that are similar by AA?

Back

ΔABC ∼ ΔDEF.