1.4 - Pairs of Angles

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

<1 and <2

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

<1 and <3

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

<2 and <4

Finding the coordinates of a midpoint

Find the coordinates of the midpoint of segment CD with endpoints C(-2, -1) and D(4, 2)

The side across from the right angle that stretches from one leg tot he other is the _____.

Hypotenuse.

Finding distances in the coordinate plane

Use the Distance Formula to find the distance, to the nearest tenth, from A to B.

Finding distances in the coordinate plane 2

Use the Pythagorean Theorem to find the distance, to the nearest tenth, from A to B.

Vertical angles

Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. VERTICAL ANGLES are two nonadjacent angles formed by two intersecting lines. <1 and <3 and vertical angles, as are <2 and <4.

Adjacent angles

Are two angles in the same plane with a common vertex and a common side, but no common interior points. <1 and <2 are adjacent angles.

Supplementary angles

Are two angles whose measures have a sum of 180 degrees. <A and <C are supplementary.

Complementary angles

Are two angles whose measures have a sum of 90 degrees. <A and < B are complementary.

Find the measure of each of the following.

Complement of <M

Using the distance formula.

Find AB and CD. Then determine if segment AB is congruent to segment CD.

Finding the circumference and area of a circle

Find the circumference and area of the circle.

Linear

A linear pair of angles is a pair of adjacent angles whose non common sides are opposite rays. <3 and <4 form a linear pair.

Coordinate plane

A plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis).

Radius

A radius of a circle is a segment whose endpoints are the center of the circle and a point on the circle.

Find the next item in each pattern. Monday, Wednesday, Friday...

Alternating days of the week make up the pattern. The next day is Sunday.

Using complements and supplements to solve problems

An angle measures 3 degrees less than twice the measure of its complement. Find the measure of its complement.

Diameter

In a circle a diameter is a segment that passes through the center of the circle and whose endpoints are on the circle.

Diagram

In the diagram, a and b are the lengths of the shorter sides, or legs, of the right triangle. The longest side is called the hypotenuse and has length c.

In a right triangle, the two sides that form the right angle are the ___.

Legs

Find the next item in each pattern. 3, 6, 9, 12, 15

Multiples of 3 make up the pattern. The next multiple is 18.

Identifying Vertical Angles

Name one pair of vertical angles. Do they appear to have the same measure?

The location, or coordinates, of a point are given by an _____ ____ (x, y).

Ordered pair

You can also use the ______ ____ to find the distance between two points in a coordinate plane.

Pythagorean Theorem

Find the measure of each of the following.

Supplement of <N

Area

The area A of a plane figure is the number of nonoverlapping square units of a given size that exactly cover the figure.

Base

The base b can be any side of a triangle.

Circumference

The circumference of a circle is the distance around the circle.

You can find the midpoint of a segment by using...

The coordinates of its endpoints. Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Height

The height h is a segment from a vertex that form a right angle with a line containing the base. The height may be a side of the triangle or in the interior or the exterior of the triangle.

Perimeter

The perimeter P of a plane figure is the sum of the side lengths of the figure.