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Geometry - Fundamental Ideas - Page 1

Document preview content for Geometry - Fundamental Ideas

Geometry - Fundamental Ideas

This document provides study materials related to Geometry - Fundamental Ideas. It may include explanations, summarized notes, examples, or practice questions designed to help students understand key concepts and review important topics covered in their coursework.

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Geometry - Fundamental Ideas - Page 1 preview imageStudy GuideGeometry–Fundamental Ideas1. Angles and Angle PairsFigure 1∠BACWhat Is an Angle?Anangleis formed bytwo rays that share the same endpoint.•The shared endpoint is called thevertex.•The two rays are called thesides of the angle.•Angles are measured indegrees (°).•A degree measure is always between0° and 180°.For example, if raysABandACmeet at pointA, then:•Ais the vertex.•ABandACare the sides of the angle.How Do We Name Angles?There are several correct ways to name the same angle. Let’s look at them.
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Geometry - Fundamental Ideas - Page 2 preview imageStudy GuideFigure 2Different names for the same angle.By the VertexIf there is only one angle at point A, we can call it:By a Number or Letter Inside the AngleSometimes angles are labeled with a number or lowercase letter.By Three PointsThis is the most common method.Important: Themiddle letter is always the vertex.Example1:Renaming AnglesFigure 3Different names for the same angle
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Geometry - Fundamental Ideas - Page 3 preview imageStudy Guide•Angle 3 can also be named∠IMJor∠JMI.•∠KMJ is the same as∠4.Different names—but the same angle!1.2Measuring Angles: The Protractor PostulateFigure 4Using the Protractor PostulateThis rule helps us measure angles correctly.If pointOis on a line, every ray starting atOcan be matched with a number between0° and 180°.To find the measure of an angle:1.Find the numbers that match each ray.2.Subtract the smaller number from the larger number.If(a > b), then:Example2:Finding Angle MeasuresUsing a protractor scale:
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Geometry - Fundamental Ideas - Page 4 preview imageStudy GuideFigure 5Using the Protractor Postulate(a) Find m∠SON(b) Find m∠ROT(c) Find m∠MOEAlways subtract the smaller reading from the larger one.Figure 6Addition of angles.
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Geometry - Fundamental Ideas - Page 5 preview imageStudy Guide1.3Adding Angles: The Angle Addition PostulateIf a ray lies between two other rays, you can add the smaller angles to get the larger angle.If ray OB lies between OA and OC, then:Think of it like putting two small pieces together to make one bigger piece.Example3:Adding Angle MeasuresIf:Figure 7Addition of angles.•(m∠1 = 32°)•(m∠2 = 45°)And one ray lies between the others, then:So:
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Geometry - Fundamental Ideas - Page 6 preview imageStudy Guide1.4Angle BisectorAnangle bisectoris a ray that divides an angle intotwo equal angles.Figure 8Bisector of an angleIf ray OY bisects∠XOZ, then:Important Fact:An angle that is not a straight angle hasexactly one bisector.1.5Special Types of AnglesAngles are grouped based on their measure.Right Angle
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Geometry - Fundamental Ideas - Page 7 preview imageStudy GuideFigure 9A right angle.•Measures exactly90°•Marked with a small square•All right angles are equalAcute AngleFigure 10An acute angle.
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Geometry - Fundamental Ideas - Page 8 preview imageStudy Guide•Less than90°•Small and sharpObtuse AngleFigure 11An obtuse angle.•More than90°•Less than180°Straight AngleFigure 12A straight angle
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Geometry - Fundamental Ideas - Page 9 preview imageStudy Guide•Exactly180°•Forms a straight lineSome textbooks simply call this astraight angle.Example4:Classifying AnglesFigure 13Classification of anglesLet’s identify each angle type.(a)∠BFDRight angle(b)∠AFEStraight angle(c)∠BFCAcute angle
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Geometry - Fundamental Ideas - Page 10 preview imageStudy Guide(d)∠DFAObtuse angleSummary•An angle forms when two rays share a vertex.•Angles measure between 0°and 180°.•Always subtract smaller from larger when measuring.•You can rename angles in multiple ways.•Angles can be added together.•An angle bisector splits an angle into two equal parts.•Special angle types: acute, right, obtuse, straight.2. Special AnglesSome pairs of angles have special names. These names depend on:•Where the angles are located•Or what their measures add up toLet’s break each type down in a simple way.2.1Adjacent AnglesAdjacent anglesare two angles that:
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Document Details

University
Texas A&M University
Course
Geometry
Subject
Mathematics

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