section 1-4
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Section 1-4. Angles. Angle – figure formed by 2 rays that have the same endpoint. The rays are the _______. The common endpoint is the _________. When naming an angle, use __ letters, __ letter, or ___ number. Vertex = ______ Name the angle.Sides = ____ and ____. sides. vertex. - PowerPoint PPT PresentationTRANSCRIPT
Section 1-4Angles
Angle – figure formed by 2 rays that have the same endpoint.
The rays are the _______.
The common endpoint is the _________.
When naming an angle, use __ letters, __ letter, or ___ number.
Vertex = ______Name the angle. Sides = ____ and ____
sides
vertex
3 11
point B
�⃗�𝐴 �⃗�𝐶ABC, CBA, 4, B
Name 3 angles.
ABD, DBC, ABC
Angles are measured in _________.There are 4 classifications of angles._______________ _______________Measures between Measure ____________ and _____
________________ _______________Measures between Measure _____________ and _______
degrees
acute right
straightobtuse
0° 90°90°
90° 180°180°
Protractor Postulate: Given QOP, if is paired with x and is paired with y, then mQOP = .Example 1 20° and 90°Example 2 90° and 120°Example 3 90° and 40°
= 70° = 30° = 50°
Angle Addition Postulate: If point B lies in the interior of AOC, then mAOB + mBOC = mAOC.
Angle Addition Postulate: If AOC is a straight angle, then mAOB + mBOC = 180°.
Find x, mABC, mCBD.
Angle Addition PostulatemABC + mCBD = mABD
7x + 2x = 1809x = 180
x = 20
mABC = (7x)°mABC = 7(20)mABC = 140°
mCBD = (2x)°mCBD = 2(20)mCBD = 40°
Find x and the other angle measures.
Angle Addition Postulate(3x + 4) + (2x – 4) = 90
3x + 4 + 2x – 4 = 90
x = 18
(3x + 4)°3(18) + 4
58°
(2x – 4)°2(18) – 4
32°5x = 90
congruent angles – angles that have ___________________________
adjacent angles – 2 angles in a _______ that have a _________ ________ and a _________ ______, but no common interior points
equalmeasures
planecommon vertex common side
adjacent
adjacent
nonadjacentnonadjacent
nonadjacent
bisector of an angle – a ______ that divides an angle into 2 _____________ angles
Ex. Given: bisects BED, mAEB = (19x)°, mBEC = (8x + 20)°Find x and mCED.
raycongruent
(19x)°(8x + 20)°
(8x + 20)°
(19x) + (8x + 20) + (8x + 20) = 18019x + 8x + 20 + 8x + 20 = 180
35x + 40 = 18035x = 140
x = 4
mCED = (8x + 20)°mCED = 8(4) + 20mCED = 52°
Examples:Give another name for each angle. 1. DEB 2. CBE 3. BEA 4. DAB 5. 7 6. 9
∠ 4 8 3
1 C,ECB,
ABEDCB,DCA, ECA
7. m1 + m2 = m______ 8. m3 + m4 = m______ 9. m5 + m6 = m______ or ______
EAB
AEC
EDC 180°
10. Name the vertex of 3. 11. Name the right angle.
point B
8 or BED
State another name for each angle. 12. 1 13. 6 14. EBD 15. 4
A or BAE
BDC
3
DBC
16. BDE or BDA 17. 2 18. 5 19. 9
ABE
7
C or BCD
BEA
HOMEWORK:page 21 #2-34 even