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19. Adjacent angles Two angles that lie in the same plane, have a common vertex and side but no common interior points. Examples of adjacent angles: DOC and COB AOB and BOC Angles that are not adjacent: DOC and AOB http://cdn-1.ask-math.com/images/adjacent-angle.png
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1.5 Angle RelationshipsThen: You measured and classified angles.Now:1. Identify and use special pairs of angles 2. Identify perpendicular lines.
http://resource.rockyview.ab.ca/t4t/math103/images/m5/m10_3_m5_110_opt.jpeg
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSfcWPCNbrY9EJ1Sk8kdE_5MpYgvwVsr4ENawGoma_QmfzzRoSb
http://concepts.ck12.org/preview/complementary-angles.jpg
19. Adjacent anglesTwo angles that lie in the same plane, have a common vertex and side but no common interior points.
Examples of adjacent angles: DOC and COB
AOB and BOC
Angles that are not adjacent: DOC and AOB
http://cdn-1.ask-math.com/images/adjacent-angle.png
20. Linear pairA pair of adjacent angles whose noncommon sides are opposite rays.
Example of a linear pair: DAC and CAB
Angles that are not a linear pair: DAC and DAB
http://www.icoachmath.com/image_md/Linear_Pair2.jpg
21. Vertical AnglesTwo nonadjacent angles formed by two intersecting lines.
Examples of vertical angles
1 and 3
2 and 4
Vertical angles are congruent.http://www.freemathhelp.com/images/lessons/angles5.gif
Example 1: Name an angle pair that satisfies each condition:
a. Two acute adjacent angles ______ and ______
b. A linear pair ______ and ______
c. Two obtuse vertical angles ______ and ______
22. Complementary Angles
Two angles with measures that have a sum of 90.
Example complementary angles: CBD and DBE
Complementary angles do not have to be adjacent.
23. Supplementary Angles
Two angles with measures that have a sum of 180.
Examples of supplementary angles: ABC and CBE
EFG and GFH
Supplementary angles do not have to be adjacent.Linear pair of angles are supplementary.
Example 1 continued:Name an angle pair that satisfies each condition:
d. Angle complementary to EKH ______
e. Angle supplementary to FKG ______
Example 2: a. Find the measure of an angle and its complement if one
angle measures 24 degrees more than the other.
Sketch:
Solution:
Example 2c: Find value of x and y.
1. Relationship between NSP and PSQ:2. Relationship between NSQ and MSN:3. Find value of x:
4. Relationship between NSQ and MSR:
5. Find value of y:
Example 2: Find the value of the variable.
e. mABC = (6x + 19)mCBD = (x)
f. mABC = (5p + 28)mDBE = (12p)
24. Perpendicular lines Lines, segments, or rays that form
four right angles. Form congruent adjacent angles Symbol:
http://math.info/image/421/perpendicular_lines.jpg
Example 3: Find x and y so that and are perpendicular.
1. Find x.
2. Find y.
Interpreting Diagrams
Example 4:Determine whether each statement can be assumed from the figure.
a. mVYT = 90.
b. TYW and TYU are supplementary.
c. VYW and TYS are adjacent.
1.5 Assignmentp. 51-54
#8-40 evens, 43-45, 49, 50, 57-60
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