1. Lesson 5-2 Use perpendicular bisectors
Geometry
Lesson 5-2
Use perpendicular bisectors

2. Learning Target
You will use perpendicular bisectors to solve problems.

3. 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.

4. 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 C D B E

5. 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

9. 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.

10. 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

11. 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 = r, find r, q, and m HWP. H P X A Q W
8q q + 90 = 180
9q = 63
q = 7
6r + 4 = r
3r = 18
r = 6
m HWP = 17

12. Circumcenters Acute triangles: it is in the triangle
Obtuse: it is outside of the triangle
Right: it is on the triangle

13. Together
Page 306 # 3,11, 13,17,20

14. Homework
Page # 4-16 even