Triangle Inequalities, Hinge Thm, and Bisectors

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is: 2 < x < 12.

Front

What does the Hinge Theorem state?

Back

The Hinge Theorem states that if 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, then the third side of the first triangle is longer than the third side of the second triangle.

Front

How can you use the Hinge Theorem to compare two triangles?

Back

You can compare the lengths of the third sides of two triangles by examining the lengths of the two sides and the included angles.

Front

What is the Converse of the Hinge Theorem?

Back

The Converse of the Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

Front

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the range of possible values for the third side of a triangle with sides 8 and 10?

Back

The range is: 2 < x < 18.

Front

What is a bisector in a triangle?

Back

A bisector in a triangle is a line segment that divides an angle into two equal parts.

Front

How does the angle bisector theorem work?

Back

The angle bisector theorem states that the ratio of the lengths of the two segments created by the bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Front

If a triangle has angles of 30°, 60°, and 90°, which angle is the largest?

Back

The largest angle is 90°.