4-4: 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 \( \Delta ABC \cong \Delta DEF \), what can we conclude about the sides and angles?

Back

If \( \Delta ABC \cong \Delta DEF \), then all corresponding sides and angles are equal: \( \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, \overline{CA} \cong \overline{FD} \) and \( \angle A \cong \angle D, \angle B \cong \angle E, \angle C \cong \angle F \).

Front

Given \( \Delta PIG \cong \Delta COW \), what is the corresponding side to \( WO \)?

Back

The corresponding side to \( WO \) is \( GI \).

Front

If \( \Delta ABC \cong \Delta DEF \), what is the corresponding side to \( \overline{CA} \)?

Back

The corresponding side to \( \overline{CA} \) is \( \overline{FD} \).

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that certain properties (sides and angles) are equal, which can be used to solve problems and prove other geometric theorems.

Front

If \( \Delta ABC \cong \Delta XYZ \), is it true that \( \overline{AC} \cong \overline{XZ} \)?

Back

TRUE. If two triangles are congruent, then all corresponding sides are also congruent.

Front

What is the first step in proving triangles are congruent?

Back

The first step in proving triangles are congruent is to identify the criteria for congruence, 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 the SSS criterion state?

Back

The SSS (Side-Side-Side) criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does the SAS criterion state?

Back

The SAS (Side-Angle-Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the ASA criterion state?

Back

The ASA (Angle-Side-Angle) criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.