Define congruence in the context of geometry.

Congruence means same size and shape.

• Figures match perfectly.

• Can be moved or flipped.

• No gaps or overlaps exist.

What does the symbol \( \cong \) represent in geometric terms?

The symbol indicates congruence.

• Shows figures are identical.

• Corresponding sides equal in length.

• Corresponding angles equal in measure.

Explain the concept of corresponding parts in congruent figures.

Corresponding parts match in congruent figures.

• Angles and sides align precisely.

• Congruence indicates equal measures.

• Essential for proving figure similarity.

Fill in the blank: Rigid transformations include translation, reflection, and ___.

Rotation

What is the significance of the CPCTC principle in geometry?

CPCTC shows triangle congruence relationships.

• Establishes side-angle congruence.

• Supports proofs in geometric problems.

• Essential for triangle comparisons.

True or False: The AAA criterion guarantees that two triangles are congruent.

False. The AAA criterion only indicates that two triangles are similar, meaning they have the same shape but not necessarily the same size.

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60°, what congruence criterion can be used to determine if triangle DEF with DE = 5 cm, DF = 7 cm, and angle D = 60° is congruent to triangle ABC?

SAS postulate confirms congruence.

• Two sides equal in length.

• Included angle is also equal.

• Proves triangles are congruent.

Riddle: I can be transformed by sliding, flipping, or turning, yet my size and shape remain unchanged. What am I?

A geometric figure undergoing a rigid transformation.

What does the SSS Congruence Postulate state?

The SSS Postulate defines triangle congruence.

• All sides equal in length.

• Establishes triangle similarity.

• Key principle in geometry.

Fill in the blank: The concept of congruence applies to all polygons, but it is particularly simple for ___.

Triangles