Similar and Congruent Figures Concepts

Rachel explains how to determine if similar figures are congruent. She discusses the properties of similar figures, which have the same angles and proportional sides, and congruent figures, which have the same angles and equal sides. Using 45-45-90 triangles as an example, she demonstrates how to check for congruence by measuring the sides. If the sides are equal, the figures are congruent; otherwise, they are only similar.

What is the main difference between similar and congruent figures?

• Similar figures are always congruent.

• Similar figures have different angles, congruent figures have the same angles.

• Similar figures have proportional sides, congruent figures have equal sides.

• Similar figures have equal sides, congruent figures do not.

Which of the following is true about similar figures?

• They have different angles and proportional sides.

• They have the same angles and equal sides.

• They have different angles and equal sides.

• They have the same angles and proportional sides.

What is a key characteristic of similar figures?

• They have equal sides.

• They have no proportionality.

• They have different angles.

• They have proportional sides.

If two triangles are similar, what must be true about their angles?

• The angles are equal.

• The angles are supplementary.

• The angles are different.

• The angles are complementary.

Which of the following is a property of similar figures?

• No proportionality

• Proportional sides

• Different angles

• Equal sides

What does it mean for two figures to be congruent?

• They have different angles and proportional sides.

• They have different angles and equal sides.

• They have the same angles and equal sides.

• They have the same angles and proportional sides.

Which statement is true for congruent figures?

• They have different sides.

• They have different angles.

• They have proportional sides.

• They have equal angles and sides.

What must be true for two figures to be congruent?

• They must have different sides.

• They must have different angles.

• They must have equal sides and angles.

• They must have proportional sides.

In a 45-45-90 triangle, what is the relationship between the sides?

• The sides are in the ratio 1:2:2.

• The sides are in the ratio 1:1:1.

• The sides are in the ratio 1:2:√3.

• The sides are in the ratio 1:1:√2.

What is the angle measure in a 45-45-90 triangle?

• 60, 60, 60 degrees

• 45, 45, 90 degrees

• 30, 60, 90 degrees

• 90, 90, 90 degrees