pre-algebra 5.5 coordinate geometry. complete each sentence. 1. two lines in a plane that never meet...
TRANSCRIPT
Complete each sentence.
1. Two lines in a plane that never meet are called lines.
2. lines intersect at right angles.
3. The symbol || means that lines are .4. When a transversal intersects two lines, all of the acute angles are congruent.
parallel
Perpendicular
parallelparallel
Warm Up
The slope of a horizontal line is 0. The slope of a vertical line is undefined.
slope =vertical change
horizontal change= rise
run
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
A. XY
positive slope;
slope of XY = = –5–4
54
Example: Finding the Slope of a Line
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
B. ZA
negative slope;
slope of ZA = = ––1 2
12
Example: Finding the Slope of a Line
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
C. BC
slope of BC is undefined
Example: Finding the Slope of a Line
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
D. DM
slope of DM = 0
Example: Finding the Slope of a Line
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
A. AB A
C
B
D
FE
HG
positive slope;
slope of AB = 1 8
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B. CD
slope of CD is undefined
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
A
C
B
D
FE
HG
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C. EF
slope of EF = 0
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
A
C
B
D
FE
HG
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D. GH
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
A
C
B
D
FE
HG
negative slope;
slope of GH = = ––1 3
13
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Slopes of Parallel and Perpendicular Lines
Two lines with equal slopes are parallel.
Two lines whose slopes have a product of –1 are perpendicular.
Which lines are parallel? Which lines are perpendicular?
slope of EF = 32
slope of GH = 35
slope of PQ = 35
slope of QR = or –1 3 –3
2 3
slope of CD = or – –2 3
Example: Finding Perpendicular Line and Parallel Lines
The slopes are equal. =35
35
The slopes have a product
of –1: • – = –132
2 3
GH || PQ
EF CD
Which lines are parallel? Which lines are perpendicular?
Example Continued
A
C
B
D
F
E
K
JH
G
Which lines are parallel? Which lines are perpendicular?
slope of AB = or –6 4
–3 2
slope of CD = –2 3
slope of EF = or –4 6
–2 3
slope of GH = 23
slope of JK = or 1 3 3
Try This
CD || EF
GH AB
A
C
B
D
F
E
K
JH
G
Which lines are parallel? Which lines are perpendicular?
The slopes are equal. =–2 3
–2 3
The slopes have a product
of –1: • – = –123
3 2
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Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
parallelogram
CD || BA and BC || AD
Example: Using Coordinates to Classify Quadrilaterals
B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
parallelogram, rectangle, rhombus, square
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
TU || SR and ST || RU
TURU, RURS, RSST and STTU
Example: Using Coordinates to Classify Quadrilaterals
C. G(1, –1), H(1, –2), I(3, –3), J(3, 1)
trapezoid
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
GH || JI
Example: Using Coordinates to Classify Quadrilaterals
D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0)
parallelogram, rectangle
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
WZ || XY and WX || ZY
WZZY, ZYXY, XYWX and WXWZ
Example: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3)
parallelogram
A
CB
D
CD || BA and BC || AD
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B. E(1, 5), F(7, 5), G(6, 1), H(2, 1)
trapezoid
E F
H G
EF || HG
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This
C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4)
parallelogram, rectangle, rhombus, square
X
W
Y
Z
ZW || YX and WX || ZY
WXZW, XYWX, YZXY and ZWYZ
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This
D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1)
parallelogram, rectangle R
S
U
T
TU || SR and ST || RU
TURU, RURS, RSST and STTU
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This
Determine the slope of each line.
1. PQ
2. MN
3. MQ
4. NP
5. Which pair of lines are parallel?
1
8
7
– 10 3
MN, RQ
Lesson Quiz
D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0)
parallelogram, rectangle
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
WZ || XY and WX || ZY
WZZY, ZYXY, XYWX and WXWZ
Example: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3)
parallelogram
A
CB
D
CD || BA and BC || AD
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B. E(1, 5), F(7, 5), G(6, 1), H(2, 1)
trapezoid
E F
H G
EF || HG
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This
C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4)
parallelogram, rectangle, rhombus, square
X
W
Y
Z
ZW || YX and WX || ZY
WXZW, XYWX, YZXY and ZWYZ
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This
D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1)
parallelogram, rectangle R
S
U
T
TU || SR and ST || RU
TURU, RURS, RSST and STTU
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Try This