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Bellwork

Clickers. Bellwork. The sum of two numbers is 90 and one is 4 times the other. Write an equation and solve to find the two numbers. Bellwork Solution. The sum of two numbers is 90 and one is 4 times the other. Write an equation and solve to find the two numbers.

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Bellwork

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  1. Clickers Bellwork • The sum of two numbers is 90 and one is 4 times the other. Write an equation and solve to find the two numbers

  2. Bellwork Solution • The sum of two numbers is 90 and one is 4 times the other. Write an equation and solve to find the two numbers

  3. Quiz on WednesdayTest on Tuesday

  4. Measure and Classify Angles & Describe Angle Pair Relationships Section 1.4 & 1.5

  5. The Concept • Today we’re going to discuss the different kinds of angles • We’re also going to talk about adding and bisecting angles • We’ll also going to further that understanding by talking about special angle pair relationships

  6. Definition • Angle • Object that is created by the connection of two rays at the same endpoints • Consists of two sides and a vertex • Named by three points (of which one is the vertex) or just by the vertex if it is not shared with another angle • Object that is created by the connection of two rays at the same endpoints • Consists of two sides and a vertex • Named by three points (of which one is the vertex) B Angle 1.4 A C Indicates angle Axis of symmetry Vertex

  7. Congruence • Similar to our look at line segments, we have to be aware of the difference in use of the congruence and equals signs

  8. Protractor Postulate • The measure of an angle (denoted m) is equal to the absolute value of the difference between the real numbers for the two rays as they cross a protractor • In other words, if you measure an angle with a protractor we can be reasonably certain that it’s correct…

  9. Classification B • There are four kinds of angles • Acute • Measuring less than 90 degrees • Right • Measuring 90 degrees • Obtuse • Measuring larger than 90 degrees and less than 180 • Straight • Measuring 180 degrees A C B A C B A C A B C

  10. On your own • What kind of angle is shown below?

  11. On your own • What kind of angle is shown below?

  12. On your own • What kind of angle is shown below?

  13. Angle Addition Postulate • If P is in the interior of ∠RST, then the measure of ∠RST is equal to the sum of the measures of ∠RSP and ∠PST. R P S T

  14. Example Find the indicated angle measure R P 35 S 23 T

  15. On your own • What is the measure of angle ABD, if the measure of angle ABC is 102o? B 35o C A D

  16. Application • Find if is 72 degrees R P 3x+6 S 2x-9 T

  17. Congruency Two angles that have the same measure are considered congruent • Example 4

  18. Bisector angles • Similar to bisectors of lines, a bisector of an angle is a ray that shares the end point of a given angle that splits the measure of the angle in half R P S T

  19. Application • Find if is 32o and SP is a bisector R P S T

  20. Definition • Complementary Angles • Angles that sum to 90o • Supplementary Angles • Angles that sum to 180o Angles that sum to 90o A B Complementary Angles 1.5 D C Angles that sum to 180o B Supplementary Angles 1.5 A D C Axis of symmetry Vertex

  21. Adjacent angles • Adjacent Angles • A pair of angles that share a side R P S T • Adjacent Complementary Angles • A pair of angles that share a side that sum to 90 • Adjacent Supplementary Angles • A pair of angles that share a side that sum to 180

  22. Example • In the figure, name a pair of complementary angles, a pair of supplementary angles and a pair of adjacent angles. • Are angle KGH and angle LKG adjacent angles? Are angles FGK and angle FGH adjacent angles? Explain. G H F 131o 41o 49o K L

  23. On your own • What is the measure of ABD? B 35o C D A

  24. Linear Angle Pairs • Linear Pair • Adjacent angles whose non-common sides are opposite rays • Also supplementary angles • BAD & DAC are a linear pair D A B C

  25. Vertical Angle Pairs • Vertical Angles • Angles formed by two intersecting lines • Extended sides form opposite rays • Angle pairs are congruent • EAD & BAC are a vertical pair • EAB & DAC are a vertical pair D E A B C

  26. Uses • We can use our understanding of linear pairs and vertical angles to solve for other angles D E A 36o B C

  27. Application • Find D E A 141o B C

  28. Uses • Find all the angles D E 3x-8 A 2x-2 B C

  29. Homework • 1.4 • 3, 6, 18, 24, 26, 28, 38, 41, 42 • 1.5 • 7, 10, 14, 20-28 even, 33, 42

  30. ACT Prep • a+b=? a b 120 • a=?

  31. Practical Application

  32. Most Important Points • Complementary Angles • Supplementary Angles • Linear Pairs • Vertical Angles • Test next Tuesday

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