4B: Proving Triangles 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 congruent to two angles of another triangle, then the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity, which states that if the lengths of the corresponding sides of two triangles are proportional, 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 proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Front

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

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar by AA~.

Front

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

Back

If the ratios of the lengths of corresponding sides of two triangles are equal, the triangles are similar by SSS~.

Front

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

Back

If two sides of one triangle are in proportion to two sides of another triangle and the angles between those sides are equal, the triangles are similar by SAS~.

Front

What is the significance of corresponding angles in triangle similarity?

Back

Corresponding angles are angles that are in the same relative position in different triangles. If they are congruent, it helps establish triangle similarity.

Front

What is the significance of corresponding sides in triangle similarity?

Back

Corresponding sides are sides that are in the same relative position in different triangles. Their proportionality is essential for establishing triangle similarity.

Front

What are vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

Front

What are alternate interior angles?

Back

Alternate interior angles are pairs of angles that lie between two lines and on opposite sides of a transversal. If the lines are parallel, these angles are congruent.