Download Document

Session 2
Draw six segments that
pass through every dot in
the figure without taking
your pencil off the paper.
Warm-up: Using the Pythagorean Theorem
Find the value of x. Give
your answer in simplest
radical form.
a2 + b2 = c2
Pythagorean Theorem
22 + 62 = x2
Substitute 2 for a, 6 for b, and x for c.
40 = x2
Simplify.
Find the positive square root.
Simplify the radical.
Warmup #2: Using the Pythagorean Theorem
Find the missing side
length. Tell if the side
lengths form a Pythagorean
triple. Explain.
a2 + b2 = c2
42 + b2 = 122
b2 = 128
Pythagorean Theorem
Substitute 4 for a and 12 for c.
Multiply and subtract 16 from both sides.
Find the positive square root.
Bonus: Using the Pythagorean Theorem
Find the value of x. Give
your answer in simplest
radical form.
a2 + b2 = c2 Pythagorean Theorem
(x – 2)2 + 42 = x2 Substitute x – 2 for a, 4 for b, and x for c.
x2 – 4x + 4 + 16 = x2 Multiply.
–4x + 20 = 0 Combine like terms.
20 = 4x Add 4x to both sides.
5=x
Divide both sides by 4.
Homework
Review
Geometry
Vocabulary
Point
An exact position or location in a given plane.
Point A
or
Point B
Line
The set of points between points A and B in a plane and
the infinite number of points that continue beyond the
points.
Written as AB
Line Segment
A line with two endpoints.
Written as AB
Ray
A line that starts at A, goes through B, and continues on.
Written as
Plane
A flat, two-dimensional surface that extends infinitely far.
Angle
Formed by 2 rays coming together at a common
point (Vertex)
The angle is
ABC
Right Angle
An angle that measures 90°.
Acute Angle
An angle measuring less than 90° but greater than 0°.
Obtuse Angle
An angle measuring greater than 90° but less than 180°.
Parallel Line
Lines in a plane that either do not share any points and
never intersect, or share all points.
Written as AB PQ
Perpendicular Line
Two lines that intersect at a right angle (90°).
Written as AB  PQ
Circle
• The set of points on a plane at a certain distance,
or radius, from a single point, the center
Distance along a line
The linear distance between two points on a given line.
How far apart are the points
on the line segment?
How far apart are the points
on the line segment?
Hmmm…
CW
Vocabulary
Practice WS
Angle Addition Postulate
If B lies on the interior of AOC,
then mAOB + mBOC = mAOC.
B
A
mAOC = 115
50
O
65
C
Example 1:
D
Example 2:
G
114
K
95
19
H
Given: mGHK = 95
mGHJ = 114.
Find: mKHJ.
J
134°
A
46°
B
C
This is a special example, because the
two adjacent angles together create a
straight angle.
Predict what mABD + mDBC equals.
ABC is a straight angle, therefore
mABC = 180.
The Angle Addition Postulate
tells us:
mABD + mDBC = mABC
mGHK + mKHJ = mGHJ
95 + mKHJ = 114
mKHJ = 19.
Plug in what
you know.
Solve.
mABD + mDBC = 180
So, if mABD = 134,
46
then mDBC = ______
R
Given:
mRSV = x + 5
mVST = 3x - 9
mRST = 68
V
Find x.
S
T
Set up an equation using the Angle
Addition Postulate.
mRSV + mVST = mRST
x + 5 + 3x – 9 = 68
Solve.
4x- 4 = 68
4x = 72
x = 18
Plug in
what you
know.
Algebra Connection
Extension: Now that you
know x = 18, find mRSV
and mVST.
mRSV = x + 5
mRSV = 18 + 5 = 23
mVST = 3x - 9
mVST = 3(18) – 9 = 45
Check:
mRSV + mVST = mRST
23 + 45 = 68
B
C
mBQC = x – 7 mCQD = 2x – 1 mBQD = 2x + 34
Find x, mBQC, mCQD, mBQD.
mBQC = x – 7
mBQC = 42 – 7 = 35
Q
D
mBQC + mCQD = mBQD
x – 7 + 2x – 1 = 2x + 34
3x – 8 = 2x + 34
x – 8 = 34
x = 42
Algebra Connection
Slide 5
mCQD = 2x – 1
mCQD = 2(42) – 1 = 83
mBQD = 2x + 34
mBQD = 2(42) + 34 = 118
Check:
mBQC + mCQD = mBQD
35 + 83 = 118
x = 42
mCQD = 83
mBQC = 35 mBQD = 118
HW
Angle Addition
Postulate WS