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