Exploring Similar Polygons and AA Similarity

What are the two main criteria for polygons to be considered similar?

• All sides are proportional and all angles are proportional.

• All angles are equal and all sides are equal.

• Corresponding angles are proportional and corresponding side lengths are congruent.

• Corresponding angles are congruent and corresponding side lengths are proportional.

What does the symbol '~' represent in the context of similar figures?

• It indicates that the figures are similar.

• It indicates that the figures are equal.

• It indicates that the figures are congruent.

• It indicates that the figures are proportional.

In the example of quadrilaterals, what is the ratio of the sides AB to WX?

• 3

• 2

• 4

• 5

How do you determine which angles are congruent in similar triangles?

• By checking if the triangles are right-angled.

• By comparing the lengths of the sides.

• By measuring the angles directly.

• By looking at the order of the letters in the similarity statement.

What is the first step in solving for a missing side length in similar quadrilaterals?

• Measure all the sides.

• Check if the quadrilaterals are congruent.

• Calculate the area of the quadrilaterals.

• Label the corresponding angles that are congruent.

What does the Angle-Angle (AA) similarity criterion state?

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

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

• If all three angles of one triangle are congruent to all three angles of another triangle, then the triangles are similar.

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

In the example with triangles JLK and QMP, what is the missing angle in triangle JLK?

• 75 degrees

• 48 degrees

• 57 degrees

• 105 degrees

What is the reason for the congruence of angles X and T in the example with parallel lines?

• Adjacent angles are congruent.

• Vertical angles are congruent.

• Corresponding angles are congruent when two parallel lines are cut by a transversal.

• Alternate interior angles are congruent when two parallel lines are cut by a transversal.

In the proof of triangle similarity, what is the reason for the congruence of vertical angles?

• Alternate interior angles are congruent.

• Adjacent angles are congruent.

• Corresponding angles are congruent.

• Vertical angles are congruent.

What is the similarity statement for triangles ABE and DCE in the proof?

• Triangle ABE is congruent to triangle DCE by SAS similarity.

• Triangle ABE is similar to triangle DCE by SAS similarity.

• Triangle ABE is congruent to triangle DCE by AA similarity.

• Triangle ABE is similar to triangle DCE by AA similarity.