1.5 Angle Relationships Then: You measured and classified angles. Now: 1. Identify and use special pairs of angles 2. Identify perpendicular lines. https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSfcWPCNbrY9EJ1Sk8kdE_5MpYgvwVsr4ENawGoma_QmfzzRoSb.

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Presentation transcript:

1.5 Angle Relationships Then: You measured and classified angles. Now: 1. Identify and use special pairs of angles 2. Identify perpendicular lines. https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSfcWPCNbrY9EJ1Sk8kdE_5MpYgvwVsr4ENawGoma_QmfzzRoSb http://resource.rockyview.ab.ca/t4t/math103/images/m5/m10_3_m5_110_opt.jpeg http://concepts.ck12.org/preview/complementary-angles.jpg

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

20. Linear pair A 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 Angles Two 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 c. Two obtuse vertical angles

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. mABC = (6x + 19) mCBD = (x) f. mABC = (5p + 28) mDBE = (12p)

24. Perpendicular lines Lines, segments, or rays that form four right angles. Form congruent adjacent angles Symbol:  𝑨𝑬  𝑫𝑩 http://math.info/image/421/perpendicular_lines.jpg

Example 3: Find x and y so that 𝑲𝑶 and 𝑯𝑴 are perpendicular. 2. Find y.

Interpreting Diagrams

Example 4: Determine whether each statement can be assumed from the figure. a. mVYT = 90. b. TYW and TYU are supplementary. c. VYW and TYS are adjacent.

1.5 Assignment p. 51-54 #8-40 evens, 43-45, 49, 50, 57-60