1. Please complete the next 3 sections of your SKILL BUILDER now. 2. Please have out your HOMEWORK to be stamped.

MONDAY 1. The side view of a roof is shown below. What is x, the height of the roof to the nearest tenth of a foot? 2. Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. To the nearest hundredth, how far apart are the two planes after they land? 3. The length of a rectangular swimming pool is 36 ft. The width is 18 ft. What is the length of the diagonal of the pool to the nearest foot? a.18 ft b.30 ft c.40 ft d.54 ft

LINES AND ANGLES

Adjacent, Vertical, Supplementary, and Complementary Angles

Adjacent angles are “side by side” and share a common ray. 45º 15º

These are examples of adjacent angles. 55º 35º 50º130º 80º 45º 85º 20º

These angles are NOT adjacent. 45º55º 50º 100º 35º

When 2 lines intersect, they make vertical angles. 75º 105º

Vertical angles are opposite one another. 75º 105º

Vertical angles are opposite one another. 75º 105º

Vertical angles are congruent (equal). 30º150º 30º

Supplementary angles add up to 180º. 60º120º 40º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Complementary angles add up to 90º. 60º 30º 40º 50º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Practice Time!

Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

#1 60º 120º

#1 60º 120º Supplementary Angles

#2 60º 30º

#2 60º 30º Complementary Angles

#3 75º

#3 75º Vertical Angles

#4 60º 40º

#4 60º 40º None of the above

#5 60º

#5 60º Vertical Angles

#6 45º135º

#6 45º135º Supplementary Angles

#7 65º 25º

#7 65º 25º Complementary Angles

#8 50º 90º

#8 50º 90º None of the above

Directions: Determine the missing angle.

#1 45º?º?º

#1 45º135º

#2 65º ?º?º

#2 65º 25º

#3 35º ?º?º

#3 35º

#4 50º ?º?º

#4 50º 130º

#5 140º ?º?º

#5 140º

#6 40º ?º?º

#6 40º 50º

PARALLEL LINES Def: line that do not intersect. Illustration: Notation: l | | m AB | | CD l m A B C D

Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking Streets: Laramie & LeClaire

Examples of Parallel Lines Streets: Belmont & School

PERPENDICULAR LINES Def: Lines that intersect to form a right angle. Illustration: Notation: m  n Key Fact: 4 right angles are formed. m n

Ex. of Perpendicular Lines Window panes Streets: Belmont and Cicero

Def: a line that intersects two lines at different points Illustration: Transversal t

Definition of Transversal In a plane, a line is a transversal iff it intersects two or more Lines, each at a different point. The lines cut by a transversal may or may not be parallel. l m Parallel Lines t is a transversal for l and m. t b c Nonparallel Lines r is a transversal for b and c. r

Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. Exterior Interior

  =  =  +  = 180   l m t

l m When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. t Interior angles lie between the two lines. Exterior angles lie outside the two lines. Alternate Interior angles are on the opposite sides of the transversal. Consectutive Interior angles are on the same side of the transversal. Alternate Exterior angles are on the opposite sides of the transversal. Corresponding angles are created when a transversal crosses parallel lines. The corresponding angles are the ones at the same location at each intersection.transversalintersection

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Vertical Angles Two angles that are opposite angles. (Kissing V’s)are . (  means CONGRUENT!) t  1   4  2   3  5   8  6   7

Vertical Angles Find the measures of the missing angles 125  ? ? 55  t 125 

Corresponding Angles Two angles that occupy corresponding positions. Top Left t Top Right Bottom Right Bottom Left 11   5 22   6 33   7 44  

Corresponding Angles Find the measures of the missing angles 145  ? t 35  145 

Alternate Interior Angles Two angles that lie between parallel lines on opposite sides of the transversal t 33   6 44  

Alternate Interior Angles Find the measures of the missing angles 82  ? t 98  82 

Alternate Exterior Angles Two angles that lie outside parallel lines on opposite sides of the transversal t 22   7 11  

Alternate Exterior Angles Find the measures of the missing angles 120  ? t 60  120 

Consecutive Interior Angles Two angles that lie between parallel lines on the same sides of the transversal t 33 +  5 = 180 44 +  6 =

Consecutive Interior Angles Find the measures of the missing angles ? t 135  45 

s t c d s || t and c || d. Name all the angles that are congruent to  1. Give a reason for each answer.  3   1 corresponding angles  6   1 vertical angles  8   1 alternate exterior angles  9   1 corresponding angles  11   9   1 corresponding angles  14   1 alternate exterior angles  16   14   1 corresponding angles

Parallel Lines Discovery Activity

1.Put a dot on the top left margin 2.On the top right count down 5 lines – make a dot – connect the dots with a straight line 3.From the dot on the left count down 5 lines – make a dot 4.From the right dot count down 5 lines and make a dot – connect these dots with a straight line 5.From the top left dot, count down 10 lines and make a dot, connect this dot with a straight line to the top right corner 6.Label the angles as you see here

1. Name a pair of same-side interior angles 2. Name a pair of same-side exterior Angles 3. Name a pair of adjacent angles 4. Name a pair of alternate-exterior Angles 5. Name a pair of alternate-interior angles

Angles Jeopardy game