Understanding Congruence in Geometry

This lesson introduces the concept of congruence in geometry, focusing on defining congruence through basic rigid motions such as translation, rotation, and reflection. The lesson includes exercises that demonstrate how to map figures using these motions to prove congruence. It also covers the properties of congruence and provides a problem set for further practice.

What is the definition of congruence as introduced in the lesson?

• Two figures are congruent if they have the same perimeter.

• Two figures are congruent if they have the same area.

• Two figures are congruent if they are similar in shape.

• Two figures are congruent if they can be mapped onto each other using a sequence of rigid motions.

Which symbol is used to denote congruence between two figures?

• The equal sign (=)

• The approximately equal sign (≈)

• The congruence symbol (≅)

• The similarity symbol (~)

What does the example with figure S and S' demonstrate about congruence?

• Congruence is reversible through the opposite sequence of rigid motions.

• Congruence can be achieved through scaling.

• Congruence requires only translation.

• Congruence is not reversible.

In Exercise 1, what sequence of motions is used to show S1 is congruent to S2?

• Rotation and scaling

• Reflection and scaling

• Translation, rotation, and reflection

• Translation and scaling

What is the purpose of Exercise 1 in the lesson?

• To demonstrate the concept of similarity

• To show congruence through a sequence of rigid motions

• To calculate the area of geometric figures

• To explore the properties of angles

What is the main focus of Exercise 2?

• Performing a sequence of scaling and reflection

• Performing a sequence of translation and rotation

• Calculating the perimeter of a figure

• Exploring the properties of parallel lines

What does Exercise 2 demonstrate about the properties of congruence?

• Congruence preserves the size and shape of figures

• Congruence does not preserve angles

• Congruence requires at least three transformations

• Congruence only applies to triangles

What is one of the basic properties of congruence mentioned in the lesson summary?

• Congruence maps lines to curves

• Congruence preserves the lengths of segments

• Congruence changes the size of angles

• Congruence only applies to circles

What should students do if they find the first problem in the problem set tricky?

• Skip the problem and move on

• Check the answer key for guidance

• Ask a friend for the answer

• Guess the answer and move on

What is the notation used for congruence in geometry?

• Equal sign with a squiggle above it

• Equal sign with a tilde above it

• Equal sign with a dot above it

• Equal sign with a line above it