Unit III: SECTION #1 - Angles & Lines

Transcription

1 1/16 Name Period An angle is made up of two rays that meet at a point called the vertex. Kinds of Angles 1) Acute Angle the angle s measure is between 0ᵒ and 90ᵒ 2) Right Angle the angle s measure is 90ᵒ

2 2/16 3) Obtuse Angle the angle s measure is between 90ᵒ and 180ᵒ 4) Straight Angle the angle s measure is 180ᵒ 5) Reflex Angle the angle s measure is between 180ᵒ and 360ᵒ

3 3/16 Identify the type of angle: acute, right, obtuse, straight or reflex. 1) 123ᵒ 2) 215ᵒ 3) 265ᵒ 4) 68ᵒ 5) 89ᵒ 6) 32ᵒ 7) 180ᵒ 8) 327ᵒ 9) 171ᵒ 10) 99ᵒ 11) 140ᵒ 12) 195ᵒ

4 4/16 Supplementary & Complementary Angles Supplementary angles are 2 angles that add up to 180ᵒ. Complementary Angles are 2 angles that add up to 90ᵒ. Complete the chart. If there is no complement or supplement explain why. Angle Complement Supplement 75ᵒ 43ᵒ 103ᵒ 87ᵒ 300ᵒ 45ᵒ 78ᵒ 112ᵒ 160ᵒ 220ᵒ

5 5/16 Practice A. Identify the type of angle: acute, right, obtuse, straight or reflex. 1) 145ᵒ 2) 15ᵒ 3) 90ᵒ 4) 98ᵒ 5) 286ᵒ 6) 130ᵒ B. Complete the chart. If there is no complement or supplement explain why. Angle Complement Supplement 78ᵒ 25ᵒ 125ᵒ 93ᵒ 145ᵒ

6 6/16 UNIT III SECTION #2 - Lines and Angles Transversal a line that cuts through 2 or more lines Alternate Interior Angles on opposite sides of the transversal but in between the two lines cut by the transversal. - These angles are only equal when the two lines cut by the transversal are parallel. Examples: Examples:

7 7/16 Name the transveral(s) and the pairs of alternate interior angles. 1) 2) l! l! Alternate Exterior Angles on opposite sides of the transversal but outside the two lines cut by the transversal Examples:

8 8/16 Name the transversal(s) and the pairs of alternate exterior angles. 1) 2) Corresponding Angles on the same side of the transversal and formed by the transversal and different lines. - these angles are only equal when the lines are parallel Examples:

9 9/16 Name the transversal and the pairs of corresponding angles. 1) 2) l! l! l! m n Vertically Opposite Angles when two lines intersect these angles are always across from each other - these angles are always equal

10 10/16 Practice: 1. a) Name the transveral. b) Name a pair of corresponding angles. c) Name a pair of alternate exterior angles. d) Name a pair of vertically opposite angles. e) Name a pair of alternate interior angles.

11 11/16 2. a) Name the transveral. b) Name a pair of corresponding angles. c) Name a pair of alternate exterior angles. d) Name a pair of vertically opposite angles. e) Name a pair of alternate interior angles. c

12 12/16 Find the measure of the indicated angles when the lines are not parallel Remember the lines are not parallel so: only vertically opposite angles are equal and two angles that make a straight angle are supplementary (add up to 180 ) 1) m 1 = 125 and m 8 = 100

13 13/16 2) m 4 = 38 and m 5 = 73 3) m 3 = 88, m 6 = 45, and m 12 = 137

14 14/16 Find the measure of the indicated angles when the lines are parallel Remember the lines are parallel so: alternate interior angles are equal corresponding angles are equal co-interior angles are supplementary (or consecutive interior angles are supplementary or interior angles on the same side of the transversal are supplementary) 1)

15 15/16 2) 3)

16 16/16 4) m A = 120 and l! l2 l! l! 5) m 10 = 84