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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Transparency 5a. Lesson 1-5. Learners will be able to identify and use. special pairs of angles and perpendicular lines. Adjacent angles :.

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Transparency 5

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  1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

  2. Transparency 5a

  3. Lesson 1-5 Learners will be able to identify and use special pairs of angles and perpendicular lines.

  4. Adjacent angles: are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points.

  5. Vertical angles: are two nonadjacent angles formed by two intersecting lines

  6. Linear pair: is a pair of adjacent angles whose noncommon sides are opposite rays.

  7. Answer: The angle pairs that satisfy this definition are Example 5-1a Name two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.

  8. Example 5-1b Name two acute vertical angles. There are four acute angles shown. There is one pair of vertical angles. Answer: The acute vertical angles are VZY and XZW.

  9. Name an angle pair that satisfies each condition. a. two acute vertical angles b. two adjacent angles whose sum is less than 90 Example 5-1c Answer:BAC and FAE,CAD and NAF, or BAD and NAE Answer:BAC and CAD or EAF and FAN

  10. Complementary angles: are two angles whose measures have a sum of 90.

  11. Supplementary angles: are two angles whose measures have a sum of 180.

  12. Example 5-2a ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle. Explore The problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180. Plan Draw two figures to represent the angles.

  13. Example 5-2b Let the measure of one angle be x. Solve Given Simplify. Add 6 to each side. Divide each side by 6.

  14. Example 5-2c Use the value of x to find each angle measure. Examine Add the angle measures to verify that the angles are supplementary. Answer: 31, 149

  15. Example 5-2d ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other. Answer: 16, 74

  16. Perpendicular lines: intersect to form four right angles.Intersect to form congruentadjacent angles. Is readis perpendicular to

  17. ALGEBRA Find x so that . Example 5-3a

  18. If , then mKJH 90. To find x, use KJI and IJH. Sum of parts whole Answer: Example 5-3b Substitution Add. Subtract 6 from each side. Divide each side by 12.

  19. ALGEBRA Find x and y so that and are perpendicular. Answer: Example 5-3c

  20. Determine whether the following statement can be assumed from the figure below. Explain. mVYT = 90 The diagram is marked to show that From the definition of perpendicular, perpendicular lines intersect to form congruent adjacent angles. Answer: Yes; and are perpendicular. Example 5-4a

  21. Example 5-4b Determine whether the following statement can be assumed from the figure below. Explain. TYW and TYU are supplementary. Answer: Yes; they form a linear pair of angles.

  22. Example 5-4c Determine whether the following statement can be assumed from the figure below. Explain.VYW and TYSare adjacent angles. Answer: No; they do not share a common side.

  23. Determine whether each statement can be assumed from the figure below. Explain. a. b.TAU and UAY are complementary. c.UAX and UXA are adjacent. Example 5-4d Answer: Yes; lines TY and SX are perpendicular. Answer: No; the sum of the two angles is 180, not 90. Answer: No; they do not share a common side.

  24. Homework:Lesson 1-5, p. 41# 8-22,24-34 even,41, 43

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