Chapter 3 Student Notes Chapter 3 Test Friday, October 12 th

3.1 Parallel Lines and Transversals

Parallel Lines AB C D

Skew Lines and Parallel Planes Two lines are skew if they l m l and m are ________

Examples 1. Name all segments that are parallel to AD 2. Name all segments that intersect AD 3. Name all segments that are skew to AD 4. Name all planes that are parallel to plane ABC. Answers: 1. ___________________ 2. ___________________ 3. ___________________ 4. ___________________

t Transversal – ___________________________ Exterior Angles – _____________________ Interior Angles – _____________________ l m

l m t Consecutive Interior Angles – _____________________ Alternate Exterior Angles – _____________________ Alternate Interior Angles –_____________________ Corresponding Angles – _____________________

r s Name the transversal that forms each pair of angles. Then name the special name for each pair. 1.  3 &   11 &   17 &  1 4.  2 &  3 5.  4 &  6 ____ __________________ TransversalSpecial Angle Pair Name p q

3-2 Angles and Parallel Lines

m n t If m ║ n, then the following relationships exists:

m n t If m ║ n, then: Corresponding  ’s  Alternate Interior  ’s  Alternate Exterior  ’s  Consecutive Interior  ’s supplementary

If m  1 = 70 o, find the others. 70 o

More Examples 1. The value of x, if m  3 = 4x + 6 and m  11 = 126. If line AB is parallel to line CD and s is parallel to t, find: 2. The value of x, if m  1 = 100 and m  8 = 2x The value of y, if m  11 = 3y – 5 and m  16 = 2y + 20.

Important Notes: When the lines are parallel; The acute angles ____________________. The obtuse angles ___________________. One acute angle is _______________ to one obtuse angle m n t

1 30 o 36 o Find the measure of angle 1.

1 140 o 30 o Find the measure of angle 1.

Find the value of x and y. (5y + 10) o (10y + 5) o (5x) o

(5x + 7) 0 (8x + 4) 0 (2y) 0 (5x + 12) 0 (6y + 8) 0 (6x + 4) 0 Find x and y.

3-3 Slopes of Lines

Slope of ǁ, and ⊥ lines

Determine if each pair of lines are ǁ, ⊥, or neither. 1.Line 1, m = -2 Line 2, m = ½ 2. Line 3, m = 3 Line 4, m = 3 3. Line 5, m = 4/3 Line 6, m = 3/4 4. Line 7, m = -1 Line 8, m = 1

Find the slope of each line. 1. l 2. m 3.Any line ǁ to l. 4.Any line ⊥ to m. l m

Slope of a Line The slope of the non-vertical line through the points and is m = The slope of a vertical line ____________. The slope of a horizontal line is _______.

Find the slope of the line through the given points. (-4, 7) and (3, 7) Examples

Find the slope of the line through the given points. (3, -1) and (3, 2) Examples

Find the slope of the line through the given points. (1, -4) and (2, 5) Examples

Find the slope of the line through the given points. (-2, 5) and (1, -1) Examples

Given each pair of points, Determine if AB ǁ CD, AB ⊥ CD, or neither. 1.A(-3, -2) B(9, 1) C(3, 6) D(5, -2) 2.A(5, -4) B(10, 0) C(9, -8) D(5, -13)

l m m( l ) = m( m ) = m( s ) = m ( r ) = r s

1.m = 3, passes through (2, 1) 2.Passes through (-4, -5)  the line that passes through MN, M(-1, -3), N(-3, 4) Graph each line described below. m(MN) = m(  ) =

3-5 Proving Lines Parallel

Postulate 3-4 l m t if, then ______. If ___________________________________________________ corresponding angles are congruent, then the _________________.

Theorem 3-5 l m t if, then ______. If ________________________________________________________ alternate exterior angles are congruent, then the ___________________.

Theorem 3-6 l m t if, then ______. 1 2 If __________________________________________________________ consecutive interior angles are supplementary, then ____________________.

Theorem 3-7 l m t if, then ______. If ____________________________________________________ alternate interior angles are congruent, then ________________.

Theorem 3-8 l m t if, then ______.

Determine which pair of lines is parallel and why p q rs 1.  1   8 2.  7    11   9 4. m  6 +  10 = 180

Find x so that l || m 110 o (5x +10) o l m

Find x so that l || m (5x + 15) o (6x -10) o l m

Find x so that l || m (5x–7) o (7x–5) o l m

Find x so that l || m (7x–1) o l m

3.6 Perpendiculars and Distance

How would you measure the distance from Fishersville to the Beach? Fishersville Beach

Draw the segment that represents the distance from P to AB. P BA P BA

P BA P BA

P B A P B A