Congruent Figures

What are congruent triangles?

• Triangles that have the same angles.

• Triangles that have the same perimeter.

• Triangles that have the same area.

• Triangles that have the same shape and size.

State the criteria for congruent triangles.

• Corresponding sides and angles are equal.

• The lengths of the sides are equal.

• The sum of the angles is equal.

• Corresponding sides and angles are not equal.

If two angles of one triangle are congruent to two angles of another triangle, can we conclude that the triangles are congruent? Why or why not?

• No

• Yes, because congruent angles imply congruent triangles.

• Yes, because congruent angles imply congruent sides.

• Yes, because congruent angles imply congruent areas.

What is the symbol used to represent congruence?

• =

• ~

• +

• ≡

If two sides of one triangle are congruent to two sides of another triangle, can we conclude that the triangles are congruent? Why or why not?

• Yes, because congruent sides imply congruent triangles.

• Yes, because congruent sides and angles imply congruent triangles.

• No

• No, because congruent sides do not necessarily imply congruent triangles.

What is the difference between congruent triangles and similar triangles?

• Congruent triangles have the same size but different shapes.

• Similar triangles have the same size and shape.

• Congruent triangles have the same shape but different sizes.

• Congruent triangles have the same shape and size, while similar triangles have the same shape but different sizes.

If two triangles are congruent, are their corresponding angles and sides also congruent? Explain.

• Yes

• No, only the sides are congruent.

• No, only the angles are congruent.

• No, neither the angles nor the sides are congruent.

What is the angle-side-angle (ASA) congruence criterion?

• A congruence criterion that states if two triangles have two corresponding angles not congruent and the included side congruent, then the triangles are congruent.

• A congruence criterion that states if two triangles have two corresponding angles congruent and the included side not congruent, then the triangles are congruent.

• A congruence criterion that states if two triangles have two corresponding sides congruent and the included angle congruent, then the triangles are congruent.

• A congruence criterion that states if two triangles have two corresponding angles congruent and the included side congruent, then the triangles are congruent.

What is the side-angle-side (SAS) congruence criterion?

• A congruence criterion that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

• A congruence criterion that states if two sides and the included angle of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

• A congruence criterion that states if two angles and the included side of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

• A congruence criterion that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

What is the side-side-side (SSS) congruence criterion?

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

• If the sum of the squares of two sides of one triangle is equal to the square of the third side, then the two triangles are congruent.

• If the medians of one triangle are congruent to the corresponding medians of another triangle, then the two triangles are congruent.

• If all three sides of one triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.