Geometry Unit 10

Diameter

A chord that passes through the center of the circle. The diameter is twice the length of the radius.

Circle

A circle contains 360 degrees.

Chord

A line segment with both endpoints on the circle.

Radius

A line segment with one endpoint on the center of the circle and one endpoint on the circle. The radius is half the diameter.

Major Arc

A major arc travels more than 180 degrees around a circle.

Minor Arc

A minor arc travels less than 180 degrees around a circle.

Triangle

A triangle contains 180 degrees.

Isosceles Triangle

A triangle with two congruent sides. The base angles are congruent. Any triangle formed with two of the sides being radii of the circle will be isosceles.

Central Angle

An angle whose vertex is on the center of the circle. The sides are radii. The central angle is equal to the measure of the arc it intercepts.

Inscribed Angle

An angle whose vertex is on the circle. The sides are chords. The inscribed angle is half the measure of the arc it intercepts.

Intercepted Arc

An arc that is formed by an inscribed or central angle. The itercepted arc is double the measure of an inscribed angle, and equal in measure to a central angle.

Semicircle

Half of a circle. It is exactly 180 degrees.

Sides of a triangle

The longest side of a triangle lies opposite the largest angle. The shortest side of a triangle lies opposite the smallest angle.

Pythagorean Theorem

This is used to find missing sides of a right triangle.

Area of a Triangle

This is used to find the area of a triangle.

Distance Formula

This is used to find the distance between two points.

Midpoint Formula

This is used to find the midpoint of a line segment.

Area of a Sector

To find the area of a sector, multiply the Area of the circle by the number of degrees in the arc divided by 360.

Length of an Arc

To find the length of an arc, multiply the Circumference of the circle by the number of degrees in the arc divided by 360.

Congruent Chords

Two chords with equal measures. Congruent chords will be equidistant from the center of the circle. Congruent chords will form congruent arcs and congruent central angles.

Central and Inscribed Angles Intercepting the Same Arc

When a central angle and an inscribed angle intercept the same arc, the inscribed angle will be half the measure of the central angle.

Thale's Theorem

When an angle is inscribed in a semicircle, it is a right angle. The hypotenuse of the triangle will always be a diameter of the circle.

Parallel Chords

When two chords of a circle are parallel, the arcs intercepted on both ends will be the same measure.

Inscribed Angles Intercepting the Same Arc

When two inscribed angles intercept the same arc, they are congruent.

Parallel Lines

When two lines are parallel, their slopes are equal.

Perpendicular Lines

When two lines are perpendicular, their slopes are negative reciprocals.