Understanding Congruent Triangles

What are congruent triangles?

• Triangles that have different sizes but the same angles.

• Triangles that are identical in color and texture.

• Congruent triangles are triangles that have the same size and shape, with all corresponding sides and angles equal.

• Triangles that have one side equal and the other two sides different.

How can you tell if two triangles are congruent?

• Two triangles are congruent if they have the same area.

• Two triangles are congruent if they have one angle equal and one side equal.

• Two triangles are congruent if they are both equilateral.

• Two triangles are congruent if they satisfy SSS, SAS, ASA, AAS, or HL criteria.

What is the significance of corresponding sides in congruent triangles?

• Corresponding sides in congruent triangles are different in length.

• Corresponding sides in congruent triangles are proportional but not equal.

• Corresponding sides in congruent triangles can vary in size.

• Corresponding sides in congruent triangles are equal in length.

What is the Angle-Side-Angle (ASA) criterion for triangle congruence?

• 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.

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

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

• If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

What does the Side-Angle-Side (SAS) criterion state?

• Two triangles are congruent if three sides of one triangle are equal to three sides of another triangle.

• Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

• Two triangles are congruent if one side and two angles of one triangle are equal to one side and two angles of another triangle.

• Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Can two triangles be congruent if they have different orientations?

• Yes, two triangles can be congruent with different orientations.

• Two triangles can only be congruent if they are identical in shape and size.

• Congruent triangles cannot be rotated or flipped.

• No, congruent triangles must have the same orientation.

What is the Side-Side-Side (SSS) criterion for triangle congruence?

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

• If one side of a triangle is equal to one side of another triangle, the triangles are congruent.

• If two angles of one triangle are equal to two angles of another triangle, the triangles are congruent.

• If the perimeter of one triangle is equal to the perimeter of another triangle, the triangles are congruent.

How do you use the Hypotenuse-Leg (HL) theorem for right triangles?

• The HL theorem states that if two right triangles have a congruent hypotenuse and one congruent leg, then the triangles are congruent.

• The HL theorem states that two triangles are congruent if they have two congruent legs.

• The HL theorem applies only to isosceles triangles.

• You can use the HL theorem for any type of triangle.

What role do transformations play in understanding congruence?

• Congruence is determined solely by side lengths.

• Transformations only apply to non-congruent figures.

• Transformations have no effect on the shape of figures.

• Transformations illustrate that congruent figures can be made to overlap through operations like translation, rotation, and reflection.

Can congruent triangles have different sizes?

• Congruent triangles can have different angles.

• Congruent triangles can vary in area but not shape.

• Yes, congruent triangles can be different sizes.

• No, congruent triangles cannot have different sizes.