Warm-up 1.Draw and, where A, B, and C are non-collinear. 2. What do we name this geometric figure?
Angles and Angle Measures Day 1 Section 2.1 What kind of angles do you see in the two blankets?
Rays Part of a line that starts at an endpoint and extends forever in one direction To name a ray, use its endpoint and any other point on the ray AD H
An angle is formed by 2 non-collinear rays that have a common end point. The rays are the sides of the angle. The common endpoint is the vertex. Slides You can name the angle in the figure to the right: angle ABC or ABC angle CBA or CBA angle B or B angle 1 or 1
Example 1: Angles Naming 3
The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle. Angle Name:
The measure of an angle is the smallest amount of rotation about the vertex from one ray to another, measured in degrees. The geometry tool used to measure an angle is a protractor. Slides
What type of angle is used to shoot the pool ball in to the hole?
Angles - Measurement How do you measure an angle? 1. Place the center mark of the protractor on the vertex. 2. Line up the 0 mark with one side of the angle. 3. Read the measure on the protractor scale.
Find the measure of each angle. Then classify each as acute, right, or obtuse. Example 2: Measuring and Classifying Angles A. WXV B. ZXW
Congruent angles are angles that have the same measure. Arc marks are used to show that the two angles are congruent. Slides
An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Slides Example:
Example 3 KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.
Example 4 OB bisects AOC, mAOB = (3x + 16)°, and mBOC = (8x – 14)°. Find mAOB. A O C B
Example 5: BD bisects ABC, mABD = (6x + 4)°, and mDBC = (8x – 4)°. Find mABD.
Slides m DAC + m CAB = m DAB. So, m DAB = 35° + 30° = 65°. Example:
Example 6: In the diagram, 1 is congruent to 2. Use the information below to find the value of x. m 1 = x + 12, m 3 = 6x – 4
Example 7: BD bisects ABC, mABD = (5x - 3)°, and mDBC = (3x + 15)°. Find mABC.
Review: 1.When do you set the angle measures equal to solve for the variable? 2.Do the order of the letters matter when you name an angle? Why or why not? 3.Do the lengths of the sides of an angle affect its measure?