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Similar to the angle pairs power point presentation
the angle pairs power point presentation
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- 2. Measurement of anAngle 2
- 3. To denote themeasure of an angle we write an “m” in front of the symbol for the angle. Here are some common angles and their measurements. 3 1 2 3 4 1 45 m 2 90 m 3 135 m 4 180 m
- 4. Congruent Angles • So,two angles are congruent if and only if they have the same measure. • So, The angles below are congruent. 4 if and only if . A B m A m B Means Congruent Means Equal
- 5. Types of Angles •An acute angle is an angle that measures less than 90 degrees. • A right angle is an angle that measures exactly 90 degrees. • An obtuse angle is an angle that measures more than 90 degrees. 5 acute right obtuse
- 6. • A straightangle is an angle that measures 180 degrees. (It is the same as a line.) • When drawing a right angle we often mark its opening as in the picture below. 6 straight angle right angle Types of Angles
- 7. Perpendicular Lines • Twolines are perpendicular if they intersect to form a right angle. See the diagram. • Suppose angle 2 is the right angle. Then since angles 1 and 2 are supplementary, angle 1 is a right angle too. Similarly, angles 3 and 4 are right angles. • So, perpendicular lines intersect to form four right angles. 7 1 2 3 4
- 8. Perpendicular Lines • Thesymbol for perpendicularity is • So, if lines m and n are perpendicular, then we write . . m n m n m n
- 9. Adjacent Angles Adjacent anglesshare a common vertex and one common side. Adjacent angles are “side by side” and share a common ray. 45º 15º
- 10. Adjacent Angles These areexamples of adjacent angles. 55º 35º 50º 130º 80º 45º 85º 20º
- 11. Adjacent Angles These anglesare NOT adjacent. 45º 55º 50º 100º 35º 35º
- 12. Vertical Angles • Twoangles formed by intersecting lines and have no sides in common but share a common vertex. • Are congruent. When 2 lines intersect, they make vertical angles. 75º 75º 105º 105º Common Vertex
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- 15. Vertical angles arecongruent (equal). 30º 150º 150º 30º Vertical Angles
- 16. Vertical Angles 1 4 Two angles that are opposite angles. Vertical angles are congruent. 1 2 3 4 5 6 7 8 2 3 5 8, 6 7 Name the Vertical Angles
- 17. Supplementary Angles Add upto 180º. 60º 120º 40º 140º Adjacent and Supplementary Angles
- 18. Supplementary Angles • Twoangles are supplementary if their measures add up to • If two angles are supplementary each angle is the supplement of the other. • If two adjacent angles together form a straight angle as below, then they are supplementary. 18 180 . 1 2 1 and 2 are supplementary
- 19. Complementary Angles Add upto 90º. 70º 20º 20º 70º Adjacent and Complementary Angles
- 20. Complementary Angles • Twoangles are if their measures add upcomplementary to • If two angles are complementary, then each angle is called the complement of the other. • If two adjacent angles together form a right angle as below, then they are complementary. 20 90 . 1 2 A B C 1 and 2 are complementary if is a right angle ABC
- 21. Supplementary vs. Complementary Howdo I remember? The way I remember is this: • C comes before S in the alphabet. • 90 comes before 180 when I count. • Complementary is 90, Supplementary is 180.
- 22. Guess Who? • Iam an angle.
- 23. Guess Who? • Iam an angle. • I have 180°
- 24. Guess Who? • Iam an angle. • I have 180° • I look like this:
- 25. Guess Who? • Iam an angle. • I have 180° • I look like this: Supplementary Complementary
- 26. Guess Who? • Iam two adjacent angles.
- 27. Guess Who? • Iam two adjacent angles. • I look like an “L” with a line in the middle.
- 28. Guess Who? • Iam two adjacent angles. • I look like an “L” with a line in the middle. • I add up to 90° • I look like this:
- 29. Guess Who? • Iam two adjacent angles. • I look like an “L” with a line in the middle. • I add up to 90° • I look like this: Complementary Supplementary
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- 36. Find the missingangle 55 x I know that these angles are complementary. They must add up to 90° So…… 90 – 55 = 35 The missing angle is 35
- 37. You try. 20 x Are they supplementaryor complementary? Find the missing side.
- 38. You try. 20 x Are they supplementaryor complementary? complementary Find the missing side. 90 – 20 = 70 The missing angle Is 70
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- 40. Find the missingangle 120 x I know these are supplementary angles. Supplementary angles add up to 180. The given angle is 120. So….. 180 – 120 = 60 The missing angle is 60
- 41. Find the missingangle 130 x What kind of angles? What’s the missing angle?
- 42. Find the missingangle 130 x What kind of angles? Supplementary What’s the missing angle? Adds up to 180, so….. 180 – 130 = 50
- 43. Find the missingangle x 30 Do this one on your own.
- 44. Directions: Identify each pairof angles as adjacent, vertical, supplementary, complementary, or none of the above.
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- 74. Transversal • Definition: Aline that intersects two or more lines in a plane at different points is called a transversal. • When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n
- 75. Corresponding Angles Corresponding Angles:Two angles that occupy corresponding positions. 75 2 6 1 2 3 4 5 6 7 8 1 5 3 7 4 8 The corresponding angles are the ones at the same location at each intersection
- 76. Angles and ParallelLines • If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles
- 77. Proving Lines Parallel •If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. D C B A
- 78. Alternate Angles • AlternateInterior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. Lesson 2-4: Angles and Parallel Lines 78 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6 7 8
- 79. Example: If lineAB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. Lesson 2-4: Angles and Parallel Lines 79 m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80° t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
- 80. Proving Lines Parallel •If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. D C B A
- 81. Ways to ProveTwo Lines Parallel • Show that corresponding angles are equal. • Show that alternative interior angles are equal. • In a plane, show that the lines are perpendicular to the same line.
- 82. Homework Pg 305 #6-14e,18-32e (just answers) Pg 309 #6-24e (just answers)