1.4 - During: Measuring Angles I will find and compare the measures of angles.

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Presentation transcript:

1.4 - During: Measuring Angles I will find and compare the measures of angles.

Key Concept: Angle DefinitionHow to Name ItDiagram An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. You can name an angle by: Its vertex, _____ A point on each ray and the vertex, _____ or _____ A number, _____

 The interior of an angle is the region containing all of the points between the two sides of the angle.  The exterior of an angle is the region containing all of the points outside of the angle.

Problem: Naming Angles  What are two other names for <1?

Problem: Naming Angles A. What are two other names for <KML? B. Would you be correct to name any of the angles <M? Explain.

 One way to measure the size of an angle is in degrees. To indicate the measure of an angle, write a lowercase m in front of the angle symbol.  In the diagram below, the measure of <A is 62. You write _______________.

Key Concept: Types of Angles Acute AngleRight AngleObtuse Angle Straight Angle An angle whose measure is less than 90 degrees. An angle whose measure is equal to 90 degrees. An angle whose measure is greater than 90 degrees. An angle whose measure is equal to 180 degrees.

Problem: Measuring and Classifying Angles  What are the measures of <LKN, <JKL, and <JKN? Classify each angle as acute, right, obtuse, or straight.

Problem: Measuring and Classifying Angles  What are the measures of <LKH, <HKN, and <MKH? Classify each angle as acute, right, obtuse, or straight.

 Angles with the same measure are congruent angles.  This means that if m<A = m<B, then <A ______ <B. You can also say that if <A ______ <B, then m<A = m<B  You can mark angles with arcs to show that they are congruent. If there is more than one set of congruent angles, each set is marked with the same number of arcs.

The Angle Addition Postulate is similar to the Segment Addition Postulate. Postulate 1-8 Angle Addition Postulate If point B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC.

Problem: Using the Angle Addition Postulate  If m<RQT = 155, what are m<RQS and m<TQS?

Problem: Using the Angle Addition Postulate  <DEF is a straight angle. What are m<DEC and m<CEF?

Problem: Using the Angle Addition Postulate  If m<ABC = 175, what are m<ABD and m<CBD?

After: Lesson Check  Use the diagram for Questions 1 – What are two other names for <1? 2. If m<ABD = 85, what is an expression to represent m<ABC? 3. Classify <ABC.

Homework Page 31, #6 – 20 even, all, all