Measuring Angles

ESSENTIALS OF GEOMETRY

C. N. ColnGeometrySt. Barnabas HSBronx, NYRays and AnglesCh. 1.5 and 1.6 A RAY consists of a point on a line and all points on one side of the point. DEFINITION OF A RAYKADThis ray can be called AK or ADThe beginning of the name is the endpoint, A. DEFINITION OF OPPOSITE RAYSOpposite rays are two rays of the same line with a common endpoint and no other points in commonRAYRAYCTA

Oh, Mrs. C, you are tooooooo funny!

ANGLESThis is an angle DEFINITION OF AN ANGLEAn angle is a set of points that is the union of two rays having the same endpoint AnSideSideVertexDEThere are several ways to name this angle: A DAE EAD n6In this case there is no confusion you name an angle by the vertex.AA DEFINITION OF AN ANGLEBIG ANGLE VS. LITTLE ANGLEobtuse angleacute angleAngleABCDHow many angles do you see?A 1B 2C 3D Huh?DEFINITION OF DEGREEDegrees were developed by the Babylonians thousands of years ago. They divided a circle into 360 parts and called each part one degree.Notation for angle measurementThe symbol for degrees, as you probably already know, is a small superscript circle.4537112WHAT IS A PROTRACTOR?

MEASURING AN ANGLE

This is an acute angle and it measures 61MEASURING AN ANGLE

This is an obtuse angle and it measures 127

The measure of angle BVA is:A: 180B: 125C: 50D: 25ANGLE CONGRUENCE

Angles are congruent if they have the same measure.AB17ANGLE ADDITION POSTULATEIf point S is in the interior (middle) of angle PQR, then the measure of PQS + measure of SQR = measure of PQRPQRSBISECTOR OF AN ANGLEPQRSThe bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent angles. PQS = SQR~DefinitionComplementary angles are two angles that total 90 degrees30 and ___ 27 and ___ 12 and ___ 6360 78DefinitionSupplementary angles are two angles thattotal 180 degrees and ___67 and ___124 and ___15556113AngleComplementSupplement284967100147AngleComplementSupplement28624967100147AngleComplementSupplement28621524967100147AngleComplementSupplement2862152494167100147AngleComplementSupplement2862152494113167100147AngleComplementSupplement286215249411316723100147AngleComplementSupplement286215249411316723113100147AngleComplementSupplement286215249411316723113100none147AngleComplementSupplement286215249411316723113100none80147AngleComplementSupplement286215249411316723113100none80147noneAngleComplementSupplement286215249411316723113100none80147none33DEFINITIONStraight angle is an angle that is the union of opposite rays. It makes a straight line and measures 180

DEFINITIONLinear angles are two angles that share a side and make a line. We also called them supplementary angles Linear angles total 180DEFINITIONRight angles are angles that measure 90DEFINITIONAcute angles measure less than 90DEFINITIONObtuse angles are angles that measure more than 90 but less than 180DEFINITION Perpendicular lines are lines that intersect to form right angles. The shortest distance from any point to a line is the length of the perpendicular from the point to the line.

DefinitionA reflex angle is an angle that measures more than 180ASSIGNMENTp. 18 # 3, 4 p. 21 #4-24 (e)