Geometry
Geometry
Lesson 5-2
Use perpendicular bisectors
Learning Target
•
You will use perpendicular bisectors to solve
problems.
Do we remember????
•
Do we remember what the word
perpendicular means?
•
Do we remember what the word bisect or
bisector means?
•
We will put them together to get a line that is
cut in half and a right angle.
Perpendicular bisectors and angle
bisectors
•
Perpendicular bisector
: A perpendicular bisector of a
triangle is a line, segment, or ray that passes through the
midpoint of the side and is perpendicular to the side.
•
Theorem 5.2: If AB is the perpendicular bisector of CD, then
AC is congruent to AD
.
•
Theorem
5.3: If CE = ED, then E lies on the perpendicular
bisector of CD .
A
B
C
D
E
LOOK AT PAGE 303
EXAMPLE 1
•
WHAT DOES PERPENDICULAR BISECTOR
MEAN?
•
SO WHAT DOES THAT MEAN ABOUT CD AND
AD?
•
SO HOW DO WE SOLVE THIS?
•
TRY PAGE 304 GUIDED PRACTICE #1-2
Perpendicular bisectors and angle
bisectors (cont’d)
•
Concurrent Lines
: Three or more lines that
intersect at a common point.
•
Point of concurrency
: point of intersection of
concurrent lines.
•
Circumcenter
: The point of concurrency of the
perpendicular bisectors of a triangle.
Concurrency of perpendicular
bisectors of a triangle
•
Says the perpendicular bisectors of a triangle
intersect at a point that is equidistant from
the vertices of the triangle.
–
We will draw this picture
Perpendicular bisectors and angle
bisectors (cont’d)
•
If WP is a perpendicular bisector, m WHA =
8q +17
,
m HWP = 10 + q, AP = 6r +4,
and
PH =
22 + 3r,
find
r, q,
and
m HWP.
W
H
P
Q
A
X
8q + 17 + 10 + q + 90 = 180
9q = 63
q = 7
6r + 4 = 22 + 3r
3r = 18
r = 6
m HWP = 17
Circumcenters
•
Acute triangles: it is in the triangle
•
Obtuse: it is outside of the triangle
•
Right: it is on the triangle
Together
•
Page 306 # 3,11, 13,17,20
Homework
•
Page 306-307 # 4-16 even
Explore the concept of perpendicular bisectors and how they are used in solving geometric problems. Learn about the theorems related to perpendicular bisectors and angle bisectors, concurrent lines, and the concurrency of perpendicular bisectors in triangles. Practice solving problems involving perpendicular bisectors to enhance your understanding of geometric principles.
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Presentation Transcript
Geometry Lesson 5-2 Use perpendicular bisectors
Learning Target You will use perpendicular bisectors to solve problems.
Do we remember???? Do we remember what the word perpendicular means? Do we remember what the word bisect or bisector means? We will put them together to get a line that is cut in half and a right angle.
Perpendicular bisectors and angle bisectors Perpendicular bisector: A perpendicular bisector of a triangle is a line, segment, or ray that passes through the midpoint of the side and is perpendicular to the side. Theorem 5.2: If AB is the perpendicular bisector of CD, then AC is congruent to AD. A C D B E Theorem 5.3: If CE = ED, then E lies on the perpendicular bisector of CD .
LOOK AT PAGE 303 EXAMPLE 1 WHAT DOES PERPENDICULAR BISECTOR MEAN? SO WHAT DOES THAT MEAN ABOUT CD AND AD? SO HOW DO WE SOLVE THIS? TRY PAGE 304 GUIDED PRACTICE #1-2
Perpendicular bisectors and angle bisectors (cont d) Concurrent Lines: Three or more lines that intersect at a common point. Point of concurrency: point of intersection of concurrent lines. Circumcenter: The point of concurrency of the perpendicular bisectors of a triangle.
Concurrency of perpendicular bisectors of a triangle Says the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. We will draw this picture
Perpendicular bisectors and angle bisectors (cont d) If WP is a perpendicular bisector, m WHA = 8q +17, m HWP = 10 + q, AP = 6r +4, and PH = 22 + 3r, find r, q, and m HWP. H P X A Q W 8q + 17 + 10 + q + 90 = 180 9q = 63 q = 7 m HWP = 17 6r + 4 = 22 + 3r 3r = 18 r = 6
Circumcenters Acute triangles: it is in the triangle Obtuse: it is outside of the triangle Right: it is on the triangle
Together Page 306 # 3,11, 13,17,20
Homework Page 306-307 # 4-16 even
