# 1.2 & 1.3 Classifying Angles 2.5 Angle Relationships

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1.2 & 1.3 Classifying Angles2.5 Angle RelationshipsMeasure and classify angles.Identify and use congruent angles and the bisector of an angle.Discover relationships between special pair of angles.VocabularyDegree, ray, angle, sides, vertex, interior, exterior, right angle,acute angle, obtuse angle, angle bisector. Adjacent angles, linearpair angles, vertical angles, supplementary angles &complementary angles

What is an Angle?Two rays that share the same endpoint .side BA4vertex BABC, CBAB,4side BC

Name all angles that have B as a vertex.Answer: 5, 6, 7, and ABG

a. Name all angles that have X as a vertex.Answer: 1, 2, 3, and RXBor RXNb. Name the sides of 3.Answer:c. Write another name for 3.Answer: AXB, AXN, NXA, BXA

Degrees: Measuring AnglesWe measure the size of an angle usingdegrees.Here are some examples of angles andtheir degree measurements.

Measuring angle geogebraTo measure an angle ,we use a protractor

An angle divides a plane into two parts. PointsA, D, and E lie on the angle.Points C and B lie in the interior of the angle.Points F and G lie in the exterior of theangle.G AF D C EB

Names of AnglesType of angleDescriptionAcute Anglean angle that is less than 90 Right Anglean angle that is 90 exactlyan angle that is greater than 90 Obtuse Anglebut less than 180 Straight Angle an angle that is 180 exactlyReflex Angle an angle that is greater than 180

Classify TYV as right, acute, orobtuse. TYV is marked witha right angle symbol,so measuring is notnecessary.Answer:is a right angle.

Measure each angle named and classifyit as right, acute, or obtuse.a. CZDAnswer: 150, obtuseb. CZEAnswer: 90, rightc. DZXAnswer: 30, acute

Angle BisectorAn angle bisector is a ray that dividesan angle into two equal angles.Examples

Angles that have the same measure arecongruent angles.N 025M RP25 NMP QMPQ 0

SIGNS A railroad crossing sign forms congruentangles. In the figure, WVX ZVY. If m WVX 7a 13and m ZVY 10a – 20, find the actual measurements of WVX and ZVY.Answer:

Adjacent angles are two angles that lie in thesame plane, have a common vertex, and acommon side, but no common interior points. ExamplesACBBACDDNon exampleCABD

Determine whether the following statementcan be assumed from the figure below.Explain. VYW and TYS are adjacent angles.Answer: No; they do not share a common side.

Vertical angles are angles opposite to oneanother at the intersection of two lines.(vertical angles are congruent)Non exampleExamplesAABEDEDCBC

Name two acute vertical angles.There are four acuteangles shown. Thereis one pair of verticalangles.Answer: The acute vertical anglesare VZY and XZW.

A Linear pair is a pair of adjacent angleswhose noncommon sides are opposite raysExampleBNo exampleB,D, and C are no collinearAACDCBD

Name an angle pair that satisfies each condition.a. two acute vertical anglesAnswer: BAC and FAE, CAD and NAF, or BAD and NAEb.two adjacent angles whosesum is less than 90Answer: BAC and CAD or EAF and FAN

Supplementary angles:Two angles that add up to 180 AB BDA and ADCare supplementaryCD1000BA80 0 A and Bare supplementary

Determine whether the following statement can beassumed from the figure below. Explain. TYW and TYU are supplementary.Answer: Yes; they form alinear pair of angles.

ALGEBRA Find the measures of two supplementaryangles if the measure of one angle is 6 less than fivetimes the other angle.ExploreYou know that the sumof the measures of supplementary angles is 180.PlanDraw two figures to represent the angles.

ALGEBRA Find the measures of two supplementaryangles if the measure of one angle is 6 less than fivetimes the other angle.Let the measure of one angle be x.SolveAnswer: 31, 149

Complementary angles:Two angles that add up to 90 P4012 1 and 2 arecomplementary0RQYX500Z PQR and XYZ arecomplementary

Find the measure of each letter angle

ALGEBRA Find the measures of twocomplementary angles if one anglemeasures six degrees less than fivetimes the measure of the other.Answer: 16, 74

Perpendicular lines meet to form right angles ("corner") is usedThe little symbolto indicate a right angle.is read perpendicular toBADCAD BC

ALGEBRA: Find x so that.

If IJH., then m KJH90. To find x, use KJI andSum of partswholeSubstitutionAdd.Subtract 6 from each side.Divide each side by 12.Answer:

ALGEBRA Find X and Y so thatare perpendicular.Answer:

Determine whether each statement can be assumedfrom the figure below. Explain.a.Answer: Yes; lines TY and SXare perpendicular.b. TAU and UAY arecomplementary.Answer: No; the sum of thetwo angles is 180, not 90.c. UAX and UXA are adjacent.Answer: No; they do not sharea common side.

HomeworkWorkbook 1.2 , 1.3, & 2.5

Aug 18, 2015 · Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Discover relationships between special pair of angles. Vocabulary Degree, ray, angle, sides, vertex, interior, exterior, right angle, acute angle, obtuse angle, angle bisector. Adjacent angles, linear pair angles, vertical ang

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