Hinge Theorem, Angle and Perpendicular Bisectors plus review

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 third side of the first triangle is longer than the third side of the second triangle.

Front

What does it mean for a point to be equidistant from two figures?

Back

A point is equidistant from two figures if it is the same distance from both figures.

Front

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

Back

To find the range of possible values for x in a triangle, apply 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 the relationship between angles and perpendicular bisectors?

Back

The perpendicular bisector of a segment is the locus of points that are equidistant from the endpoints of the segment, and any point on the perpendicular bisector is equidistant from the segment's endpoints.

Front

If two angles are congruent, what can be said about their measures?

Back

If two angles are congruent, their measures are equal.

Front

What is the significance of the vertex in the Hinge Theorem?

Back

In the Hinge Theorem, the vertex of the angle acts like a hinge, allowing the triangle to 'open' or 'close' based on the angle's measure.

Front

How do you calculate the length of a missing side in a triangle?

Back

To calculate the length of a missing side in a triangle, you can use the Pythagorean theorem for right triangles or the Law of Cosines for non-right triangles.

Front

What is the formula for the Hinge Theorem?

Back

The Hinge Theorem can be expressed as: If triangle ABC and triangle DEF have AB = DE, AC = DF, and angle A > angle D, then BC > EF.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, which can be proven using criteria such as SSS, SAS, ASA, AAS, or HL.

Front

What is the definition of a perpendicular bisector?

Back

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