Transcript perpendicular

We think math
is the greatest
thing ever!
What are they
talking about? If
it’s math, we
already knew it
was awesome!
What does it mean if lines are perpendicular?
They intersect to form right angles.
What is the symbol for perpendicular?

What is a segment bisector?
A segment bisector intersects a line at its
midpoint.
Use the vocabulary that you know to define
perpendicular bisector.
A perpendicular bisector intersects a line segment
at its midpoint and is perpendicular to the line
segment.
perpendicular
bisector
Perpendicular – form right angles
midpoint
Which diagram shows the perpendicular bisector of the
side of a triangle?
Line a is a perpendicular bisector of ΔXYZ.
Y
List three things that
you know about the
diagram.
a
T is the midpoint of XZ.
XT  ZT
1 and  2 are right angles
2
X
1
T
Z
a  XZ
Each side of a triangle has a perpendicular bisector. How many
perpendicular bisectors does a triangle have?
Let’s do this together
Homework#6
Graph ΔABC with A (5, 5), B (15, 5) and C (11, 17).
Find the perpendicular bisector of each side.
Start with side AB.
C
Midpoint of BC
x-coordinate = 15 + 11
2
y-coordinate = 17 + 5
2
Midpoint is (13, 11)
A
The slope of BC is
17 - 5
11 - 15
B
Slope = -12/4 = -3/1
So, the slope of the 
line is 1/3
C
Circumcenter
A
B
What do you notice about the three perpendicular
bisectors of the sides of this triangle?
Graph ΔABC with A (5, 5), B (15, 5), and C (11, 17)
Find the perpendicular bisectors of each side of the triangle.
Use the chart below to organize your work.
midpoint
AB
BC
(10,5)
(13,11)
(8,11)
-3/1
2/1
Slope of side
0
Slope of line
Perpendicular to side
undefined
-1/3
AC
-1/2
Graph the midpoint then count the slope of the
perpendicular line.
What are the coordinates of the circumcenter?
(10,10)
Okay, let’s try
another one.
Graph ΔLMN with L(-11, 4), M (-11, 14), and N (-1, 4)
Find the perpendicular bisectors of each side of the triangle.
Use the chart below to organize your work.
LN
LM
MN
midpoint
Slope of side
Slope of line
Perpendicular to side
Graph the midpoint then count the slope of the
perpendicular line.
What are the coordinates of the circumcenter?
Graph ΔXYZ with X (-11, -4), Y (-1, -14), and Z (11, -14)
Find the perpendicular bisectors of each side of the triangle.
Use the chart below to organize your work.
YZ
XZ
XY
midpoint
Slope of side
Slope of line
Perpendicular to side
Graph the midpoint then count the slope of the
perpendicular line.
What are the coordinates of the circumcenter?
What do you notice about the circumcenters of the triangles?
How are the three triangles you graphed different from each other?
What can you conclude about the location of the circumcenter of a triangle?
Acute triangle - inside the triangle
Obtuse triangle - outside the triangle
Right triangle - on the hypotenuse of the triangle
Pat found the circumcenter of ΔEFG on the outside of the triangle.
Sam classified ΔEFG as a right triangle. Pat and Sam’s teacher, Mrs.
Geometry, asked if they were looking at the same triangle. What
problem did Mrs. Geometry see?
y is the perpendicular bisector of a side of this triangle. Find the value
for each variable.
y
3x
(n² + 9)°
4x
3y + 8
4y - 1
2x
Find the value for each variable. Is line w a perpendicular bisector?
w
(9y - 7)°
(8y)°
n+2
3n - 10
3n - 2
White Note Card
Perpendicular bisectors / circumcenter
A perpendicular bisector passes through the midpoint of a segment
and is perpendicular to the segment
The intersection of the three perpendicular bisectors of the sides
of a triangle is the circumcenter of the triangle.
circumcenter
Acute triangle – inside the triangle
Right triangle – on hypotenuse
Obtuse triangle – outside the triangle