CPCTC Practice

Front

What does CPCTC stand for?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is a principle used in geometry to prove that corresponding sides and angles of congruent triangles are equal.

Front

If \( \Delta ABC \cong \Delta XYZ \), what can we conclude about the sides AB and XY?

Back

We can conclude that AB \cong XY, meaning the lengths of sides AB and XY are equal.

Front

Given \( \Delta ABC \cong \Delta DEF \), what is the relationship between \( \overline{BC} \) and \( \overline{EF} \)?

Back

Since the triangles are congruent, \( \overline{BC} \cong \overline{EF} \).

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal. This property is used to solve various geometric problems.

Front

If \( \angle C \cong \angle F \) in congruent triangles, what does this imply?

Back

This implies that the measures of angles C and F are equal.

Front

What is the definition of congruence in triangles?

Back

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure.

Front

How can you prove that two triangles are congruent?

Back

You can prove two triangles are congruent using methods such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles).

Front

What does it mean if two angles are corresponding angles in congruent triangles?

Back

Corresponding angles are angles that are in the same relative position in two different triangles. In congruent triangles, corresponding angles are equal.

Front

If \( \Delta ABC \cong \Delta DEF \), what can we say about \( \overline{CA} \)?

Back

We can say that \( \overline{CA} \cong \overline{FD} \).

Front

What is the relationship between the angles of two congruent triangles?

Back

The angles of two congruent triangles are equal; that is, if \( \Delta ABC \cong \Delta DEF \), then \( \angle A \cong \angle D \), \( \angle B \cong \angle E \), and \( \angle C \cong \angle F \).