Geometry Unit 5 CW1- Corresponding parts of congruent triangles

Front

What is a congruence statement in geometry?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, meaning they have the same shape and size. For example, if triangle ABC is congruent to triangle DEF, it can be written as \( \Delta ABC \cong \Delta DEF \).

Front

What does it mean for triangles to be congruent?

Back

Triangles are congruent if all their corresponding sides and angles are equal. This means that one triangle can be transformed into another through rigid motions such as translation, rotation, or reflection.

Front

What are corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that match up when two triangles are congruent. For example, if \( \Delta ABC \cong \Delta DEF \), then \( AB \cong DE \), \( BC \cong EF \), and \( \angle A \cong \angle D \).

Front

How do you denote congruence between two triangles?

Back

Congruence between two triangles is denoted using the symbol \( \cong \). For example, if triangle ABC is congruent to triangle XYZ, it is written as \( \Delta ABC \cong \Delta XYZ \).

Front

If \( \Delta ABC \cong \Delta XYZ \), what can be said about their angles?

Back

If \( \Delta ABC \cong \Delta XYZ \), then their corresponding angles are equal. This means \( \angle A \cong \angle X \), \( \angle B \cong \angle Y \), and \( \angle C \cong \angle Z \).

Front

What is the Side-Angle-Side (SAS) congruence criterion?

Back

The Side-Angle-Side (SAS) congruence 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 is the Angle-Side-Angle (ASA) congruence criterion?

Back

The Angle-Side-Angle (ASA) congruence 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.

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

If \( \Delta GAM \cong \Delta ERS \) and \( \overline{GA} = 11 \), what is \( \overline{ER} \)?

Back

Since the triangles are congruent, \( \overline{ER} \) is also equal to 11.

Front

What is the relationship between corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal. For example, if \( \Delta ABC \cong \Delta DEF \), then \( \angle A \cong \angle D \), \( \angle B \cong \angle E \), and \( \angle C \cong \angle F \).