Congruent Triangles

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

If \( \Delta ABC \cong \Delta XYZ \), what can we say about the sides \( \overline{AC} \) and \( \overline{XZ} \)?

Back

\( \overline{AC} \cong \overline{XZ} \) (TRUE) because corresponding sides of congruent triangles are equal.

Front

What is the significance of the symbol \( \cong \)?

Back

It denotes that two figures are congruent, meaning they are identical in shape and size.

Front

If \( \Delta EHG \cong \Delta KFC \), which pairs of sides are equal?

Back

\( EH \cong FK \), \( HG \cong KF \), \( EG \cong KC \), and \( \angle E \cong \angle C \) are all true statements.

Front

Given \( \Delta DEF \cong \Delta JKL \) and \( DE=18, EF=23, DF=9x-23, JL=7x-11 \), how do you find the value of \( x \)?

Back

Set the corresponding sides equal: \( 9x - 23 = 7x - 11 \) and solve for \( x \). The solution is \( x = 6 \).

Front

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

Back

\( \overline{BC} \cong \overline{EF} \) because corresponding sides of congruent triangles are equal.

Front

What does it mean if two angles are congruent?

Back

It means the angles have the same measure.

Front

If \( \angle A \cong \angle D \) in congruent triangles, what can we say about the other angles?

Back

The corresponding angles in congruent triangles are equal, so \( \angle B \cong \angle E \) and \( \angle C \cong \angle F \).

Front

How do you prove that two triangles are congruent?

Back

You can use criteria 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 is the relationship between the sides and angles of congruent triangles?

Back

In congruent triangles, corresponding sides are equal in length, and corresponding angles are equal in measure.