Congruent Triangles (SSS, SAS, ASA, AAS, HL)

If two triangles have two equal angles, what can be said about their sides?

• The sides opposite those angles are equal.

• The sides opposite those angles are proportional, but the triangles may not be congruent unless a third side is also equal.

• The triangles are always congruent.

• The sides opposite those angles are not related.

What does AAS stand for in triangle congruence?

• Angle-Angle-Side

• Angle-Side-Angle

• Side-Angle-Side

• Angle-Angle-Angle

What is the importance of congruence in geometry?

• Congruence helps in establishing relationships between shapes, solving problems, and proving theorems.

• Congruence is only relevant in two-dimensional shapes.

• Congruence is used to measure angles in geometry.

• Congruence has no significance in geometric proofs.

Can two triangles be congruent if they have two equal sides and a non-included angle?

• Yes, this is possible under certain conditions.

• No, this is known as SSA (Side-Side-Angle) and does not guarantee congruence.

• Yes, if the angles opposite the equal sides are also equal.

• No, this is known as ASA (Angle-Side-Angle) and guarantees congruence.

What is the relationship between similar and congruent triangles?

• Similar triangles have the same shape and size; congruent triangles have different shapes.

• Similar triangles have the same shape but not necessarily the same size; congruent triangles are both the same shape and size.

• Similar triangles are always larger than congruent triangles.

• Congruent triangles can be similar, but similar triangles cannot be congruent.

What does HL stand for in triangle congruence?

• Hypotenuse-Leg

• Height-Length

• Half-Line

• Horizontal-Line

What does SSS stand for in triangle congruence?

• Side-Side-Side: If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

• Side-Side-Angle: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

• Angle-Angle-Side: If two angles and a side of one triangle are equal to two angles and a side of another triangle, the triangles are congruent.

• Side-Angle-Side: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

How can you prove that two triangles are not congruent?

• By showing that at least one pair of corresponding sides or angles is not equal.

• By demonstrating that the triangles have the same area.

• By proving that the triangles have the same perimeter.

• By showing that all corresponding sides are equal.

What does ASA stand for in triangle congruence?

• Angle-Side-Angle

• Angle-Side-Side

• Side-Angle-Side

• Angle-Angle-Side

What are congruent triangles?

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

• Triangles that have the same area but different shapes.

• Triangles that have at least one angle equal but different side lengths.

• Triangles that are similar but not necessarily the same size.