180 likes | 270 Views
Chapter 1.4 Notes: Measure and Classify Angles. Goal: You will name, measure, and classify angles. . An angle consists of two different rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.
E N D
Chapter 1.4 Notes: Measure and Classify Angles Goal: You will name, measure, and classify angles.
An angle consists of two different rays with the same endpoint. • The rays are the sidesof the angle. • The endpoint is the vertex of the angle. • Name the angle above: _____, ______, ______ • ____________ is the vertex of the angle.
Classifying Angles: • Angles can be classified as acute, right, obtuse, and straight. • Acute angles have a measure greater than 0 and less than 90. • Right angles have a measure of 90. • Obtuse angles have a measure greater than 90 and less than 180. • Straight angles have a measure of 180.
Measuring Angles: • A protractor can be used to approximate the measure of an angle. • An angle is measured in units called degrees (o).
Postulate 3 Protractor Postulate: Consider and a point A on one side of . The rays of the form can be matched one to one with the real numbers from 0 to 180. The measure of is equal to the absolute value of the difference between the real numbers for and . A O B
Use the diagram to find the measure of the indicated angle. Then classify the angle. a.KHJ b. GHK c. GHJ d. GHL EXAMPLE 3 Measure and classify angles SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.
Postulate 4 Angle Addition Postulate: If P is in the interior of , then the measure of is equal to the sum of the measures of and . If P is in the interior of , then
Ex.4: Given that , find and .
Ex.5: If find and
Congruent Angles: • Two angles are congruent angles if they have the same measure. Angle measures ar equalAngles are congruent
Ex.8: The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If , what is ?
Ex.9: Use the diagram below. a. Identify all pairs of congruent angles. b. , , and . Find the other angle measures in the diagram.
An angle bisector is a ray that divides an angle into two angles that are congruent. Ex.10: In the diagram below, bisects , and . Find .