Proving Triangle Similarity: AA, SSS, and SAS Methods

Which of the following is NOT a criterion for proving triangle similarity?

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

• Angle-Angle (AA)

If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar by which criterion?

• Side-Side-Side (SSS)

• Angle-Angle (AA)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

What is the missing angle in a triangle if the other two angles are 48 degrees and 70 degrees?

• 58 degrees

• 72 degrees

• 60 degrees

• 62 degrees

For two triangles to be similar by the SSS criterion, what must be true about their corresponding sides?

• They must form right angles.

• They must be equal in length.

• They must be parallel.

• They must be proportional.

If the sides of two triangles are in the ratio 2:1, 2:1, and 2:1, are the triangles similar by SSS?

• No

• Yes

• Only if the angles are also congruent

• Only if the sides are equal

In the SAS similarity criterion, what must be true about the sides and the included angle?

• The sides must be proportional and the angle must be congruent.

• The sides must be equal and the angle must be congruent.

• The sides must be equal and the angle must be supplementary.

• The sides must be proportional and the angle must be supplementary.

If two triangles have sides in the ratio 5:4 and the included angle is congruent, are the triangles similar by SAS?

• Yes

• Only if the sides are equal

• No

• Only if the other angles are also congruent

What is the first step in determining if two triangles are similar by AA?

• Check if the triangles are right triangles.

• Check if one angle is congruent.

• Check if two angles are congruent.

• Check if all sides are proportional.

In a real-world problem, if a basketball player casts a shadow of 1.6 meters and a flagpole casts a shadow of 4.4 meters, what is the height of the flagpole if the player is 2 meters tall?

• 4.4 meters

• 5.5 meters

• 6.6 meters

• 3.2 meters

Why are the triangles formed by the basketball player and the flagpole similar?

• They have equal angles.

• They have equal sides.

• They have proportional sides and congruent angles.

• They are both right triangles.