Exploring AA Similarity and Triangle Relationships

What does the squiggly symbol (~) represent in geometry?

• Congruent

• Parallel

• Similar

• Equal

According to the Angle-Angle (AA) similarity theorem, what must be true for two triangles to be similar?

• All angles of one triangle are congruent to all angles of another triangle.

• Two sides of one triangle are proportional to two sides of another triangle.

• Three sides of one triangle are proportional to three sides of another triangle.

• Two angles of one triangle are congruent to two angles of another triangle.

What does the Side-Side-Side (SSS) similarity theorem state?

• If two sides of one triangle are proportional to two sides of another triangle, the triangles are similar.

• If three sides of one triangle are proportional to three sides of another triangle, the triangles are similar.

• If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

• If one angle of one triangle is congruent to one angle of another triangle, the triangles are similar.

According to the Side-Angle-Side (SAS) similarity theorem, what must be true for two triangles to be similar?

• Three sides of one triangle are proportional to three sides of another triangle.

• Two sides and the included angle of one triangle are proportional and congruent to two sides and the included angle of another triangle.

• All angles of one triangle are congruent to all angles of another triangle.

• Two angles of one triangle are congruent to two angles of another triangle.

In the given example, why are the triangles not similar when comparing 39/16 to 40/16?

• The triangles are not isosceles.

• The triangles are not right-angled.

• The angles are not congruent.

• The sides are not proportional.

When using the Side-Angle-Side (SAS) similarity theorem, what must be true about the included angle?

• It must be a right angle.

• It must be an acute angle.

• It must be congruent in both triangles.

• It must be an obtuse angle.

In the example where the sides reduce to 2/7, why are the triangles similar?

• By Angle-Side-Angle (ASA) similarity.

• By Side-Angle-Side (SAS) similarity.

• By Side-Side-Side (SSS) similarity.

• By Angle-Angle (AA) similarity.

What is the correct similarity statement for triangles that are similar by Side-Side-Side (SSS) similarity?

• The triangles are congruent.

• The triangles are similar by AA similarity.

• The triangles are similar by SAS similarity.

• The triangles are similar by SSS similarity.

In the example with parallel lines, which angles are congruent?

• Corresponding angles

• Alternate interior angles

• Vertical angles

• Adjacent angles

What is the final step to find the indicated length in the example with parallel lines?

• Subtract the lengths of the sides.

• Cross multiply and divide.

• Add the lengths of the sides.

• Use the Pythagorean theorem.