Hinge Theorem Quiz

State the Hinge Theorem.

• The Hinge Theorem applies to quadrilaterals instead of triangles.

• The Hinge Theorem states that the sum of all angles in a triangle is 180 degrees.

• If two sides of a triangle are congruent, then the third side is shorter.

• If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

What is the converse of the Hinge Theorem?

• If two sides of a triangle are congruent to two sides of another triangle, then the included angles are not congruent.

• If two angles of a triangle are congruent to two angles of another triangle, then the included sides are congruent.

• If two sides of a triangle are congruent to two sides of another triangle, then the included angles are congruent.

• If two angles of a triangle are congruent to two angles of another triangle, then the included sides are not congruent.

If two angles of one triangle are congruent to two angles of another triangle, what can you conclude?

• The triangles have equal side lengths

• The triangles are congruent

• The triangles are similar

• The third angles in both triangles are congruent.

In a triangle, if one pair of corresponding sides are congruent and the included angles are equal, what can you say about the triangles?

• The triangles are right triangles.

• The triangles are similar.

• The triangles are congruent.

• The triangles are equilateral.

Explain how the Hinge Theorem is used to prove triangles congruent.

• The Hinge Theorem is used to prove triangles congruent by comparing side lengths and included angles between two triangles.

• The Hinge Theorem is used to prove triangles congruent by comparing side lengths and corresponding angles

• The Hinge Theorem compares side lengths and opposite angles between two triangles

• The Hinge Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent

When can you apply the Hinge Theorem in a triangle?

• When the angles of one triangle are all acute angles

• When all three sides of one triangle are congruent to all three sides of another triangle

• When two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle.

• When the triangles are not similar

If two sides of one triangle are congruent to two sides of another triangle, what can you conclude?

• The triangles are congruent.

• The triangles are similar.

• The triangles are equilateral.

• The triangles are right triangles.

What is the relationship between the sides of two triangles if the angles opposite the longer sides are congruent?

• The sides are congruent

• The sides are perpendicular

• The sides are parallel

• The relationship between the sides of the two triangles is that they are proportional.

How does the Hinge Theorem help in determining the relationship between two triangles?

• The Hinge Theorem is used to find the area of the triangles based on their side lengths.

• The Hinge Theorem compares the perimeters of the triangles to determine their relationship.

• The Hinge Theorem focuses on the congruence of corresponding sides and angles in the triangles.

• The Hinge Theorem helps in determining the relationship between two triangles by comparing the side lengths and angles to establish which triangle is larger or smaller.

Under what conditions can you apply the converse of the Hinge Theorem?

• When the two sides adjacent to the angle being compared are equal in length.

• When the two sides adjacent to the angle being compared are longer on the side where the angle is larger.

• When the two sides adjacent to the angle being compared are shorter on the side where the angle is larger.

• When the angle being compared is obtuse.