LEARNING OBJECTIVE We will apply properties of perpendicular

LEARNING OBJECTIVE We will apply properties of perpendicular 1 bisectors 2 of a triangle to find missing angles and sides. Declare the Objective A: Read the objective to B. B: Define perpendicular and bisectors Definition Form an angle of 90° to a given line. 2 Cuts an object into two equal parts. 1 Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Remember the Concept Find the measure BC ACTIVATE PRIOR KNOWLEDGE 1 2 Angle Bisector Theorem-Cuts an angles into two equal parts & sides. Make the Connection Students, you already know how to find the missing sides. Now, we are going to prove and apply theorems about angle bisectors Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Example CONCEPT DEVELOPMENT Since a triangle has three sides, it has three perpendicular bisectors. The circumcenter can be inside the triangle, outside the triangle, or on the triangle. Check for Understanding In your own words, what is Circumcenter of Triangle and what does it states? “A circumcenter of a Triangle is______” Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Check for Understanding B Explain to A: What is the Angle Bisector Theorem states? Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides CONCEPT DEVELOPMENT Find m MKL Find the measure: m∠JKL Remember the Def. of bisector Concept m MKL = m JKM 3 a + 20 = 2 a + 26 a + 20 = 26 a=6 So m MKL = [2(6) + 26]° = 38° Check for Understanding A Explain to B: How did we find the m MKL? Def. of bisector -3 x -2 -x -1 -3 x -2 = -10 -1 x = 10 Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Find the measure m∠LJM, Find the measure m∠ LKM, given that m∠ JKL = 57°. given that m∠KJM = 28° Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides ? Check for Understanding A Explain to B: How did we find the m PQX? Created for Teacher Use

Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides Created for Teacher Use

SUMMARY CLOSURE Apply properties of perpendicular bisectors of a triangle to find the missing angles and sides What did you learn today about how to apply properties of perpendicular bisectors of a triangle to find the missing angles and sides? Word Bank Ø Circumcenter of a triangle Ø Circumscribed Ø Incenter of a triangle Created for Teacher Use