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.

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

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 3” B  

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 3” D B  

Lesson 1: Perpendicular Bisector Theorem Draw AC and BC in green. Measure AC and BC. Label congruent and right angle symbols. ● C 1” A 3” D B  

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

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

Lesson 2: Converse | Bisector Theorem Use your compass to make AC and BC 2” long. A 3” B  

Lesson 2: Converse | Bisector Theorem A 3” B   Converse Perpendicular Bisector Theorem: If AC = BC, then CD is the | bisector of AB.

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

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

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

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

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

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

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

7.1(a): Do I Get It? Continued Find each measure. WZ 3. RT