Topic Test 5 & 6 Review Part 2

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

How do you find the range of possible measures for the third side of a triangle?

Back

To find the range of possible measures for the third side, use the Triangle Inequality Theorem: if two sides are of lengths a and b, then the third side c must satisfy the inequalities: |a - b| < c < a + b.

Front

What is 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 significance of the circumcircle of a triangle?

Back

The circumcircle of a triangle is the circle that passes through all three vertices of the triangle, and its center is called the circumcenter.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a rule that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the difference between angle bisectors and perpendicular bisectors?

Back

Angle bisectors divide an angle into two equal angles, while perpendicular bisectors divide a segment into two equal lengths at a right angle.

Front

How do you construct a circumcircle of a triangle?

Back

To construct a circumcircle, first find the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter, which is the center of the circumcircle.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the SSS congruence rule?

Back

SSS stands for Side-Side-Side, a rule that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the purpose of constructing angle bisectors in a triangle?

Back

Angle bisectors are used to find the incenter of a triangle, which is the center of the incircle that touches all three sides.