Question

1. match the correct answer.

the hinge theorem states that if two sides of one triangle are to the corresponding two sides of a second triangle, but the included angles are not , then the third side of the triangle with the included angle will be longer.

1. match the correct answer.

the converse of the hinge theorem states that if two sides of one triangle are congruent to the corresponding two sides of a second triangle, but the third side of one triangle is than the third side of the second triangle, then the measure of the angle of the sides of the first triangle will be greater than the measure of the included angle of the sides of the second triangle.

Explanation:

Step1: Recall Hinge Theorem

The Hinge Theorem (also known as the SAS Inequality Theorem) states that if two sides of one triangle are congruent to the corresponding two sides of a second triangle, but the included angles are not congruent, then the third side of the triangle with the larger included angle will be longer. So for the first fill - in - the - blanks:

• First blank: congruent (since the two sides of one triangle are equal in length to the corresponding two sides of the second triangle)
• Second blank: congruent (the included angles are not equal, i.e., not congruent)
• Third blank: larger (the triangle with the larger included angle has the longer third side)

Step2: Recall Converse of Hinge Theorem

The Converse of the Hinge Theorem states that if two sides of one triangle are congruent to the corresponding two sides of a second triangle, but the third side of one triangle is longer than the third side of the second triangle, then the measure of the included angle of the congruent sides of the first triangle will be greater than the measure of the included angle of the congruent sides of the second triangle. So for the second fill - in - the - blanks:

• First blank: longer (the third side of one triangle is longer than the third side of the second triangle)
• Second blank: included (we are talking about the included angle of the two congruent sides)
• Third blank: congruent (the two sides of the first triangle that are congruent to the two sides of the second triangle)
• Fourth blank: congruent (the two sides of the second triangle that are congruent to the two sides of the first triangle)

Answer:

1. First blank: congruent; Second blank: congruent; Third blank: larger
2. First blank: longer; Second blank: included; Third blank: congruent; Fourth blank: congruent