5.6 Hinge Theorem Practice (with Perp. Bisectors)

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than the included angle of the other, then the side opposite the larger angle is longer.

Front

Define a perpendicular bisector.

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is the relationship between angles and sides in triangles according to the Hinge Theorem?

Back

In triangles, the larger angle is opposite the longer side, and the smaller angle is opposite the shorter side.

Front

How do you find the range of possible values for a variable in triangle inequalities?

Back

Use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is a circumcenter?

Back

The circumcenter is the point where the perpendicular bisectors of a triangle intersect, and it is equidistant from all three vertices of the triangle.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

How do you determine which angle is the largest in a triangle?

Back

The largest angle in a triangle is opposite the longest side.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is the center of mass of the triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all three sides.