Download Ch. 3

GEOMETRY – CHAPTER 3 SUMMARY
A. Vocabulary
Term
Parallel Lines
(pg 24)
Definition & symbols
Picture and/or example
Transversal
(pg 127)
Corresponding
Angles (pg 127)
Alternate
Interior Angles
(pg 127)
Same-side
Interior Angles
(Consecutive
Angles) (pg 127)
Alternate
Exterior Angles
Same-side
Exterior Angles
Geometry – Ch. 3 Summary
pg 1 of 11
Flow Proof
(pg 135)
Equiangular
triangle
(pg 148)
Acute Triangle
(pg 148)
Right triangle
(pg 148)
Obtuse triangle
(pg 148)
Equilateral
triangle (pg 148)
Isosceles Triangle
(pg 148)
Geometry – Ch. 3 Summary
pg 2 of 11
Scalene Triangle
(pg 148)
Exterior angle of
a polygon (pg
149)
Remote Interior
Angles (pg 149)
Polygon (pg 157)
Convex polygon
(pg 158)
Concave polygon
(pg 158)
Geometry – Ch. 3 Summary
pg 3 of 11
Regular Polygon
(pg 160)
Slope (pg 165)
Slope-intercept
form of a linear
equation (pg 166)
Standard form of
a linear equation
(pg 167)
Point-slope form
of a linear
equation (pg 168)
Perpendicular
Lines (pg 45)
Geometry – Ch. 3 Summary
pg 4 of 11
B. Postulates/Theorems
Name
Description
Picture and/or example
Postulate 3-1 &
Corresponding
Angles Postulate
(pg 128)
Theorem 3-1:
Alternate Interior
Angles Theorem
(pg 128)
Theorem 3-2:
Same-Side
(Consecutive)
Interior Angles
Theorem (pg 128)
Theorem 3-3:
Alternate Exterior
Angles Theorem
(pg 130)
Theorem 3-2:
Same-Side
(Consecutive)
Exterior Angles
Theorem (pg 130)
Geometry – Ch. 3 Summary
pg 5 of 11
Postulate 3-2 &
Theorems 3-5
through 3-8
(These are
converses of
Postulate 3-1 &
Theorems 3-1
through 3-4)
If two lines and a transversal form
• corresponding angles that are ____________________
• alternate interior angles that are ________________ or
• same-side (consecutive) interior angles that are ___________________
or
• alternate exterior angles that are _____________________
• same-side (consecutive) exterior angles that are ___________________
or
then the lines are __________________
Theorem 3-9
(pg 141)
Theorem 3-10
(pg 141)
Theorem 3-11
(pg 142)
Theorem 3-12
Triangle Sum
Theorem
(pg 147)
Geometry – Ch. 3 Summary
pg 6 of 11
Theorem 3-13
Triangle Exterior
Angle Theorem (pg
149)
Theorem 3-14
Polygon AngleSum Theorem (pg
159)
Theorem 3-15
Polygon Exterior
Angle-Sum
Theorem (pg 160)
Slopes of Parallel
Lines
Slopes of
Perpendicular
Lines
Geometry – Ch. 3 Summary
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pg 7 of 11
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D. Practice writing proofs:
1. Fill in the blank to complete the two-column proof.
Given :
j // k.
Prove: ∠ 2 ≅ ∠ 3
(You are proving the Alternate Interior Angles Theorem here, so do not
use it as a reason.)
€ €€
Statements
1
2
3
k
Reasons
j // k
∠1 ≅ ∠3
∠1 ≅ ∠2
€€
€€
∠2 ≅ ∠3
2.
Rewrite the above proof as a flow proof.
€€
3. Given: j // k, ∠1 ≅ ∠2
Prove: m // p
m
p
1
j
€ € €
2
k
3
Geometry – Ch. 3 Summary
j
pg 8 of 11
E. Equations of Lines:
1. Arrange the following lines in order based on the values of their slopes, from smallest to greatest.
Explain.
Line k
Line l
Line m
Line n
Line p
2. Estimate the value of the slope for each line.
a)
b)
3. Find the value of the slope for the line that passes through each pair of points. Use both formula and
graph.
a)
(2, -3) and (0, 4)
b)
(1, 5) and (1, -2)
12
10
8
6
4
2
4. Explain how to graph a line given its equation in slope-intercept form y = mx + b.
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Examples:
Graph y = 3x – 2
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Graph y = 3.
2
3
Graph y = − x + 1
€
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Graph x = - 4.
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
5. Describe step-by-step how to write the equation of a line in slope-intercept form if you have:
* A point (x1, y1) and the slope m.
Ex: Write the equation of a line with slope m =
5 and passing through the point (1, 0).
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Geometry – Ch. 3 Summary
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* Two points (x1, y1) and (x2, y2).
Ex: Write the equation of a line passing through
the points (3, -1) and (-2, 5)
a) using the point-slope form.
a) using the slope-intercept form.
* Another line parallel to it and a point on it.
Ex: Write the equation of a line that is parallel
to the line y = 2x + 5 and contains the point (1,
-3). Graph both lines.
* Another line perpendicular to it and a point on
it.
Ex: Write the equation of a line that is
perpendicular to the line y = 2x + 5 and contains
the point (1, -3).
Geometry – Ch. 3 Summary
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pg 10 of 11
F. Constructions: Using only a compass and a straightedge, construct the
following.
1.
A line parallel to a given line and through a given point that is not on the line. (pg 181)
A
j
Explain why this construction is valid.
2. A line perpendicular to a given line and
through a given point on the line. (pg 182)
3. A line perpendicular to a given line and
through a given point that is not on the line.
(pg 183)
A
j
j
Geometry – Ch. 3 Summary
pg 11 of 11