Transcript a – b - Methacton School District

Jamie Kim, Claire Jablonski, Jordan Armstrong, Jaylyn Shin,
Olivia Hoover
This bullet is a point. A star in the solar system is a
point. A pencil tip is a point.
 Points have no shape or size and is written as point P

a
pole, a pencil, and an edge of paper are all examples
of lines.
There is a line through any two points and is written as line
n or line AB or AB.
Examples
of planes in real life are sheets of paper, floor
tiles, and ceiling tiles.
 There
is exactly 1 plane between 3 points and it is written
as plane T or plane XYZ, YZX, etc. using the names of the
three non-collinear points.
What is the notation for a line segment?
Segment lengths are _________.
XY
Segments are ____________.
XY
PQ
PQ
To find the midpoint on…
a+b
A number line: ____
a and b being the endpoints of the segment.
2
A coordinate plane :
(
X1 + X2
2
)
Y1 + Y 2
,
2
(x1, X2) and (Y1, Y2) being the
coordinates of the endpoints of the segment
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A Segment Bisector is a
segment, line, or plane that
intersects a segment at its
midpoint.
(
X1 + X2 Y1 + Y2
2
,
2
)
1.
2.
3.
Set up the formula by substituting the
x coordinates of the two endpoints
where it says X2 and X1.
Do the same for the y coordinates
and Y2 and Y1.
Solve the equation.
To find the distance on a number line,
AB = I b – a I or I a – b I
a and b being the endpoints of the segment.
To find the distance between two points on a coordinate plane
use either the…
Distance Formula:
Or
Pythagorean Theorem:
 born-
c. 570 BC in Samos
 died- c. 495 BC (aged around 75) in Metapontum
 an
Ionian Greek philosopher, mathematician, and founder of the religious
movement called Pythagoreanism.
 All of what we know about him comes from what his students wrote, and
from this, we know that Pythagoras was a mathematician, philosopher,
speaker, teacher, musician, vegetarian, and religious leader who was
fascinated by the patterns of mathematics in nature
 He moved to Croton (a city in southern Italy) and started a religious and
philosophical school there
 The school’s most important discovery was that the side of a square was
shorter than the diagonal.(this showed that irrational numbers existed)
 also studied numbers and their relationships with musical harmonies
Congruent Angles:
Angle Bisector:
an interior ray that divides an angle into 2 congruent angles
1.
Adjacent Angles
2.
Vertical Angles
3.
Linear Pair
4.
Complementary Angles
5.
Supplementary Angles
6.
Perpendicular Lines
1.
A
2.
3.
87˚
9x+3
B
C
Find the measure of
angle ABC
Set the measure of angle
ABC equal to 9x+3
Solve the equation.
What is a polygon?
Draw an example.
Now draw these types of polygons!
Convex polygons:
Each interior angle is less than180 degrees.
Concave polygons:
Has an interior angle greater than 180 degrees.
Regular polygons:
Convex polygon with congruent sides and congruent angles
n-gon: a polygon with n sides
3-gon = 3 sided polygon =
=___________.
8-gon = 8 sided polygon =
= ___________.
9-gon = 9 sided polygon =
=___________.