Angle Packet

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Angle PacketName Per.:Definition: An angle is formed by two raysthat share a common endpoint.M XA 1. The point that the two rays intersect is called the .2. The two rays are called the of the angle.3. When naming angles, it is typical to use one or three letters. Sometimes one cannot useone letter. When using three letters, the must be the letter inthe middle. Other times one uses numbers to name the angles as below.M C I X K1 2A R 4. Name an angle using one letter.5. Name three different angles. , ,6. IRC can also be named in what two other ways?,An angle breaks up a plane into three regions:the exterior of the anglethe interior of the anglepoints on the angle.M 7. Name the points on the interior of FAB8. Name the points on FAB.,,,,,F ,N A S T B R Y 1

Find the measure of each angle and classify it right, acute, obtuse, or straight.a) VDSb) SDLd) SDEc) IDSIVLEDSSuppose m KNL 110 and m LNM 25 .What would you do to find the m KNM?LMKNSuppose m MNK 155 and m LNM is 30 . What would you do to find the m LNK?LMKN2

Angle Addition PostulateFor any ABC, if D is in the interior of ABC, then m ABD m DBC m ABC.Draw a diagram below to show this.Angle BisectorA that divides an angle into angles of equalis called the .1. Find m 1 if m CUB 78.B148 S2. Find m 2 if m WHI 160.EUITC42 104 2HW3. m SOX 160m 1 x 14m 2 3x – 10Find m 2SW12XOB4. m BEA 71. Find m REA.E2x R(5x 8) A3

O5. m WOV 12x. Find m LOV.W76 (5x 1) VL6. m FIE 3x, m RIE 42 , m FIR 5xFind m FIR.EFRI8. US bisects BUL, m BUS 2x 10,and m SUL 3x – 18.Find m BUL.BSULT9. m TRI 3x – 5, m IRB x 27,and m TRB 86.Does RI bisect TRB?IRB4

N10. Find the measure of each angle.a. m NEO b. m DES c. m DEO d. m SEO DO27 18 SCEComplementary and Supplementary AnglesTwo angles whose measures add up to 180⁰ are called .They can also be called a if together they form a straight angle.Two angles whose measures add up to 90⁰ are .BA50 40 CTDRIn the diagram above, and are .In the other diagram above, and are .Supplementary and Complementary AnglesFind the measures of angles 1 through 13. Mark them in your diagram.57 171 23104 455

6775 62 42 11810122 91213D14) Find m DBC.x 8x BACC15) Find m DBC.D(4x – 20) x A16)B 1 and 2 are complementary. m 1 2x 7 and m 2 4x – 19. Find the measure of eachangle.17) 3 and 4 are supplementary. m 3 5x 22 and m 4 7x 2. Find the measure of eachangle.18) Use the diagram on the right to name:a) two complementary anglesC B Db) a linear pair GEc) two adjacent angles F A6

Name Date Hour3.6 – Vertical AnglesGeometry GVertical Angles:3412THEOREM:Examples:1) Find x, y, and zx51 Yz2) Given: m 4 (2x 5) m 5 (x 30) Find: m 64563) Identify each pair of angles as adjacent, vertical, complementary, supplementary, and/or linear pair.a) 1 and 2b) 3 and 4231c) 5 and 4457

d) 3 and 54) Find x and y if CBD is congruent to FDG.5) Find each of the following:a)xb) m LATc)m TAOd) m PAO8

Vocabulary Words:Complementary AnglesAngle BisectorAdjacent Angles.Supplementary AnglesLinear PairRight AnglesVertical AnglesST bisects RSW1. In the pictures above, FOH and GOH are called .2. FOH and GOH are also called .3. Further, FOH and GOH are .4. In the pictures above, ACB and DCE are called .5. In the pictures above, JPK and KPL are called .6. JPK and KPL are also called .7. Name the vertical angle ACD to .8. What do you know about RST and TSW?9. What do you call LPM?9

In the figure, GA and GD, and GB and GE are opposite rays.10]Which angle forms a linear pair with DGC ?11]Do BGC and EGD form a linear pair?12]Name two angles that are adjacent to CGD .13]Name two angles that form a linear pair with BGD .14]Name three angles adjacent to AGB .15]Do CGE and CGB form a linear pair?16]Name the vertical angle to EGD .17]Name another pair of vertical angles. and10

Name:EDAGFCBName:1]a linear pair2]a pair of supplementary angles3]a pair of complementary angles4]a pair of adjacent angles5]a pair of vertical angles6]two right anglesWrite each pair of angles that you named above into the proper column of the tablebelow.Angle RelationshipsEqualsEquals 180 Equals 90 11

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Determine the relationship in the diagram.Are the angles complementary or is it a right angle?The angles add to 90 .Are the angles supplementary or are they a linear pair?The angles add to 180 .Do you have an angle bisector?The two angles are congruent.Do you have vertical angles?The two angles are congruent.Write the equation and then solve the equation.1.2.Equation:Equation:x x 3.4.Equation:Equation:x x 13

5.6.Equation:Equation:x x 7.8.Equation:Equation:x x 14

m ABC m ACB 3.7 – PerpendicularityNameDate HourGeometry GNOTESPerpendicularity, , and measurements gotogether.Definition: If lines, rays or segments form right angles, then they areperpendicular().What would be the converse of the definition?Examples:DE EFa bEaDFbWhat conclusions would I be able to make if given the following:AB BC1)A2)BC15

Example 1: True or False?1. PRN is acute.2. 4 83. m 5 m 6 904. QR PR5. 7 is obtuseExample 2:Find x.Example 3:Find m DBC.16

Geometry GSection 2.5. Worksheet 3NameWarm – Up:1.2.ST bisects RSW , m RST 27 m FOH m TSW m WSR 3.4.m JPK m CBF 70 & BD bisects CBF .m JPL m CBD 5.AB CDCE bisects DCBm ABC m DCE m ACD m DCB 6.m DBC m CBE BC bisects DBEm DBE 17

7.m ABE m DBC 8.BD bisects ABC andm ABD 32 m DBC m ABC 9.10.Given l pm 1 m 2 m 4 m 5 m 6 m 7 AB CDHE bisects CHBm BHG 32 m 3 m 1 m 2 m 3 m 4 m 5 m 6 m 7 18

Determine the relationship in the diagram.Are the angles complementary or is it a right angle?The angles add to 90 .Are the angles supplementary or are they a linear pair?The angles add to 180 .Do you have a angle bisector?The two angles are congruent.Do you have vertical angles?The two angles are congruent.Write the equation and then solve the equation.1.2.Equation:Equation:x x 3.4.Equation:Equation:x x m ABC m ABC 19

Geometry GSection 2.5. Worksheet 6Name5.6.Equation:Equation:x x m ABC m ABC Note: Picture is not drawn to scale.7.BD bisects ABCEquation:x 8.Equation:x 20

m ABC m EBD 21

9.Equation:x m AFD m AFB m CFD 10.11.Equation:Equation:x x m ABC m PQR m ABE m RQT 22

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Geometry GSection 2.5. Worksheet 7NameDetermine the relationship in the diagram.Are the angles complementary or is it a right angle?The angles add to 90 .Are the angles supplementary or are they a linear pair?The angles add to 180 .Do you have an angle bisector?The two angles are congruent.Do you have vertical angles?The two angles are congruent.Write the equation and then solve the equation.1.2.8x (6x 12) (7x 10) Equation:(16x 4) (18x 4) Equation:x x 3.4.(7x - 12) (16x 4) 18x (5x 18) Equation:Equation:x x m ABC m ABC 24

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2] a pair of supplementary angles 3] a pair of complementary angles 4] a pair of adjacent angles 5] a pair of vertical angles 6] two right angles Write each pair of angles that you named above into the proper column of the table below. Angle Relationships

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