3.3 notes and assignment 10-6-2014

1) Solve for x:
BELLRINGERS
-5(1-5x) + 5(-8x -2) = -4x - 8x
-5 +25x -40x - 10 = -12x
-15 -15x = - 12x
2)
-15 = 3x
x = -5
Given: 3x + 2y = 6
find the x and y intercepts and graph the line.
Find the slope of this line.
x intercept let y = 0
y intercept let x = 0
3x +2(0)=6
3)0) +2y=6
3x = 6 x = 2 (2,0)
2y = 6
y = 3 (0,3)
3) Solve the following system of equations:
19 = 5x + 2y multiply 1st equation by 2
1 = 3x - 4y
38 = 10x +4y
1 = 3x - 4y
solve for y: 1 = 3(3) -4y
1 = 9 - 4y
39 = 13x
-8 = -4y
x=3
y=2
Solution (3,2)
Homework Answers
CE
1) l parallel to p 2) post 10 3) Thm 3.2 4) thm 3.2 5) post 10 6) thm 3.2 7) thm 2.3
8) thm 3.4 9) thm 3.3 10) 4, 5, 8 = 130; 2, 3, 6, 7 = 50 11) 4,5,8 =x; 2, 3, 6, 7, = 180-x
WE
7) x =60 y = 61
8) x =10 y = 45
11) x =14 y =9
12) x = 55 y =75
9) x = 60 y =18 10) x = 70 y = 60
13) given, def of perp. lines, if 2 parallel lines are cut by a trans. then corr angles are congruent,
m<2=90, def of perpendicular lines
14) x = 56, y =100, z = 25 15) x=70;y=12;z =38 16) x=30,y=8,z=11
18) x = 25, y = 10
19) x = 30, y = 5
20 and 21 -- volunteers put these on the board
3.3 Proving Lines Parallel
Postulate 10 - If two parallel lines are cut by a transversal, then
corresponding angles are congruent.
Postulate 11 - If two lines are cut by a transversal and corresponding
angles are congruent, then the lines are parallel.
Theorem 3.5 - If 2 lines are cut by a transversal and alternate
interior angles are congruent, then the lines are parallel.
Theorem 3.6 - If 2 lines are cut by a transversal and same-side
interior angles are supplementary, then the lines are parallel
Theorem 3.7 - In a plane, 2 lines perpendicular
are parallel.
to the same line
Theorem 3.8 - Through a point outside a line, there is exactly one line
parallel to the given line.
P
k
Theorem 3.9 - Through a point outside a line, there is exactly one line
perpendicular to the given line.
P
k
Theorem 3.10 - Two lines parallel to a third line are
l m n
parallel to each other
WAYS TO PROVE TWO LINES ARE PARALLEL
(with your team, try to determine the 5 ways to PROVE
that two lines are parallel)
1) show a pair of corresponding angles are congruent
2) show a pair of alternate interior angles are congruent
3) show a pair of same-side interior angles are supplementary
4) show that both lines are perpendicular to a 3rd line
5) show both lines are parallel to a 3rd line
Proof
Given: transversal t cuts k and n; <1 ≅ < 2
Prove: k n
Proof of Theorem 3.5
Statements
1)
3
2
1
Reasons
1) given
2)
2)
3)
3)
4)
4)
If 2 lines are cut by a
transversal and corr. <s
are congruent, then the
lines are parallel.
E
V
O
PR
!
IT Try this one!!!
Given: k
t; n
Prove: k n
Statements
t
t
1
2
k
n
Reasons
Substitution
If 2 lines are cut by a
transversal and corr. <s
are congruent, then the
lines are parallel.
ASSIGNMENT
Page 87
WE 2-16 even
17-20
24-29

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