Transcript LESSONS 1-5 TO 1-9 - teachingportfolio.info

LESSONS 1-5 TO 1-7
Accelerated Algebra/Geometry
Mrs. Crespo 2012-2013
Recap
Postulate 1-5: Ruler Postulate
Postulate 1-6: Segment Addition Postulate
(AB+BC=AC)
A
B
C
Definition of Coordinate, Congruent Segments and
Midpoint.
A
B
C
-2
0
2
Lesson 1-5: Measuring Segments
Example 1
Comparing Segment Lengths
Example 2
Using Addition Segment Postulate
If AB=25, find x. Then, find AN and NB.
A
2x-6
N
AN + NB = AB
(2x-6) +( x+7) = 25
3x + 1 = 25
3x = 24
x = 24/3
x=8
x+7
B
AN = 2x – 6
= 2(8) – 6
= 16 – 6
= 10
Lesson 1-5: Examples
NB = x + 7
= 8 +7
= 15
Example 3
Using Midpoint
M is the midpoint of segment RT. Find RM, MT, and RT.
R
RM = MT
5x + 9 = 8x – 36
5x – 8x = -36 – 9
-3x = -45
x = -45/-3
x = 15
5x+9
M
RM = 5x + 9
= 5(15) + 9
= 75 + 9
= 84
8x-36
T
MT = 8x – 36
= 8(15) – 36
= 120 – 36
= 84
Lesson 1-5: Examples
RT = RM + MT
= 84 + 84
= 168
Vocabulary and Key Concepts
Postulate 1-7: Protractor Postulate
Postulate 1-8: Angle Addition Postulate
(m<AOB + m<BOC = m<AOC)
Definition of Angle
Formed by two rays with the same
endpoint.
T
B
A
O
B
Q
Lesson 1-6: Measuring Angles
C
Vocabulary and Key Concepts
Acute Angle: measures between 00 and 900
Right Angle: measures exactly 900
Obtuse Angle: measures between 900 and 1800
Straight Angle: measures exactly 1800
Congruent angles: two angles with the same measure
x0
x0
ACUTE ANGLE RIGHT ANGLE
x = 900
0 < x < 900
x0
x0
OBTUSE ANGLE STRAIGHT ANGLE
900 < x < 1800
Lesson 1-6: Measuring Angles
x = 1800
Example 1
Naming Angles
 Name can be the number between the
sides of the angle.
C
 Name can be the vertex of the angle.
 Name can be a point on one side, the
vertex, and a point on the other side
of the angle.
G
3
A
<3
<G
<AGC or <CGA
Lesson 1-6: Examples
Example 2
Measuring and Classifying Angles
 Find the measure of each <AOC.
 Classify as acute, obtuse, or straight.
C
C
B
A
B
A
O
m<AOC = 600
Lesson 1-6: Examples
O
m<AOC = 1500
Example 3
Using the Angle Addition Postulate
 Suppose that m<1=42 and m<ABC=88. Find m<2
A
m<1 + m<2 = m<ABC
42 + m<2 = 88
m<2 = 88-42
m<2 = 460
1
2
B
C
Lesson 1-6: Examples
Example 4
Identifying Angle Pairs
 In the diagram, identify pairs of numbered angles as:
Complementary angles form 900 angles.
<3 and <4
1
5
2
4
Supplementary angles form 1800 angles.
3
<1 and <2
<2 and <3
Vertical angles form an “X”.
<1 and <3
Lesson 1-6: Examples
Example 5
Making Conclusions From A Diagram
 Can you make each conclusion from a diagram?
<A ≅ <C
A
<B and <ACD are supplementary.
m<BCA + m<DCA = 1800
B
C
D
segment AB ≅ segment BC
Lesson 1-6: Examples
3
Vocabulary
Construction is using a straightedge and
a compass to draw a geometric figure.
A straightedge is a ruler with no
markings on it.
A compass is a geometric tool used to
draw circles and parts of circles called arcs.
Lesson 1-7: Basic Construction
Vocabulary
Perpendicular lines are two lines that
intersect to form right angles.
A perpendicular bisector of a segment
is a line, segment, or ray that is
perpendicular to the segment at its
midpoint, thereby, bisecting the
segment into two congruent segments.
A
D
B
C
J
An angle bisector is a ray that divides
an angle into two congruent coplanar
angles.
Lesson 1-7: Measuring Angles
K
N
L
Example 1
Constructing Congruent Segments
 Construct segment TW congruent to segment KM.
K
M
STEP 1: Draw a ray with endpoint T.
STEP 2: Open the compass the length
of segment KM.
T
STEP 3: With the same compass setting, put the compass point
on point T. Draw an arc that intersects the ray. Label the point of
intersection W.
Lesson 1-7: Examples
W
Example 2
Constructing Congruent Angles
 Construct <Y so that <Y is congruent to <G.
X
E
G
750
750
Y
F
Z
<Y ≅ <G
Lesson 1-7: Examples
1. Draw a ray with endpoint Y.
2. With the compass point on G,
draw an arc that intersects both
sides of <G. Label the points of
intersection E and F.
3. With the same compass setting,
put the compass point on point Y.
Draw an arc that intersects the ray.
Label the point of intersection Z.
4. Open the compass to the length
EF. Keeping the same compass
setting, put the compass on point
Z. Draw an arc that intersects with
the arc previously. Label the point
of intersection X.
5. Draw ray YX to complete <Y.
Example 3
Constructing The Perpendicular Bisector
 Given segment AB. Construct line XY so that line XY is
perpendicular to segment AB at the midpoint M of
segment AB.
1. Put the compass point on point
X
M
A
B
Y
Lesson 1-7: Examples
A and draw a long arc. Be sure
the opening is greater than
half of AB.
2. With the same compass
setting, put the compass point
on point B and draw another
long arc. Label the points
where the two arcs intersect as
an X and Y.
3. Draw line XY. The point of
intersection of segment AB
and line XY is M, the
midpoint of segment AB.
Example 4
Finding Angle Measures
 Line WR bisects <AWB so that m<AWR=x and
m<BWR=4x-48. Find m<AWB.
m<AWR = m<BWR
x = 4x – 48
-3x = -48
x = 16
A
R
x
4x – 48
W
m<AWR = x = 16
m<BWR = 4x – 48
= 4(16) – 48
= 64 – 48
= 16
B
So, m<AWB = m<AWR + m<BWR = 16 + 16 = 32
Lesson 1-7: Examples
HW: Posted on Edline
Accelerated Algebra/Geometry
Mrs. Crespo 2012-2013
Reference Textbook: Prentice Hall Mathematics
GEOMETRY by Bass, Charles, Hall, Johnson, Kennedy
PowerPoint Created by Mrs. Crespo
Accelerated Algebra/Geometry
Mrs. Crespo 2012-2013