Solving Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Front

If ∆ ABC ≅ ∆ DEF, what can we say about their corresponding angles and sides?

Back

If ∆ ABC ≅ ∆ DEF, then angle A = angle D, angle B = angle E, angle C = angle F, and side AB = side DE, side BC = side EF, side AC = side DF.

Front

How can you determine the length of a side in a congruent triangle?

Back

You can determine the length of a side in a congruent triangle by using the corresponding side lengths from the other triangle.

Front

What is the significance of the symbol '≅' in geometry?

Back

The symbol '≅' indicates that two geometric figures are congruent.

Front

If two triangles share a side and two angles, what can be concluded about their congruence?

Back

If two triangles share a side and two angles, they are congruent by the Angle-Side-Angle (ASA) criterion.

Front

What is the measure of an angle in a triangle if the other two angles are 40° and 75°?

Back

The measure of the third angle can be found using the triangle sum theorem: 180° - (40° + 75°) = 65°.

Front

In congruent triangles, how do the areas compare?

Back

The areas of congruent triangles are equal because they have the same size and shape.

Front

What is the relationship between the sides of a triangle and its angles?

Back

In a triangle, the larger the angle, the longer the opposite side; conversely, the smaller the angle, the shorter the opposite side.

Front

If ∆ XYZ ≅ ∆ PQR and side XY = 10 cm, what is the length of side PQ?

Back

If ∆ XYZ ≅ ∆ PQR, then side PQ is also 10 cm.