1. 7.1(a) Notes: Perpendicular Bisectors
Date:
7.1(a) Notes: Perpendicular Bisectors
Lesson Objective: Identify and use perpendicular bisectors in triangles.
CCSS: G.CO.10, G.MG.3
You will need: colored pens, CR
Real-World App: Where should a kitchen island be placed to optimize distance from the appliances?
This is Jeopardy!!!:  This is what the perpendicular bisector does to a line.

2. Lesson 1: Perpendicular Bisector Theorem
Draw AB 3” long.
A ” B

3. Lesson 1: Perpendicular Bisector Theorem
Con­struct CD as the perpendicular bi­sector of AB. Plot D at the intersection of AB and CD and point C 1” from D.
A ” B

4. Lesson 1: Perpendicular Bisector Theorem
Con­struct CD as the perpendicular bi­sector of AB. Plot D at the intersection of AB and CD and point C 1” from D.
● C 1”
A ” D B

5. Lesson 1: Perpendicular Bisector Theorem
Draw AC and BC in green. Measure AC and BC. Label congruent and right angle symbols.
● C 1”
A ” D B

6. Lesson 1: Perpendicular Bisector Theorem
A B
Perpendicular Bisector Theorem:
If CD is a | bisector of AB, then AC = BC.

7. Lesson 2: Converse | Bisector Theorem
Draw AB 3” long.
A ” B

8. Lesson 2: Converse | Bisector Theorem
Use your compass to make AC and BC 2” long.
A ” B

9. Lesson 2: Converse | Bisector Theorem
A ” B
Converse Perpendicular Bisector Theorem:
If AC = BC, then CD is the | bisector of AB.

10. Lesson 3: Using the | Bisector Theorem
Find each measure. a. b. c.

11. Lesson 4: Circumcenter Theorem
Construct the | bisector of each side of ΔABC in pencil. Label circumcenter P.
In red, draw bisectors DP, EP, and FP. Mark congruent marks and right angles also in red A
B C

12. Lesson 4: Circumcenter Theorem
Draw PA, PB and PC in blue. Anchor at P. Draw circle P with radius PA.
What do you notice about circle P? A
B C

13. Lesson 4: Circumcenter Theorem
Concurrent Lines: 3 or more lines that intersect at a common point called the Point of Concurrency.

14. Lesson 4: Circumcenter Theorem
Circumcenter: The point where the | bisec-tors of a Δ intersect. It is equidistant from each vertex of the Δ.

15. Lesson 4: Circumcenter Theorem
If P is the circumcenter of ΔABC, then PA = PB = PC. PA, PB and PC are radii of circle P.

16. 7.1(a): Do I Get It? Yes or No 1.

17. 7.1(a): Do I Get It? Continued
Find each measure.
WZ RT