Chương III. §5. Tính chất tia phân giác của một góc

Chương III. §5. Tính chất tia phân giác của một góc tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn...

Unit ANGLE BISECTOR PROPERTIES Angle Bisector Theorem  If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle Converse of the Angle Bisector Theorem  If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector Example  What is the length of line RM? Example  What is the length of FB? Independent Practice Timer Timer Aim: How can we identify properties of perpendicular bisectors? Name: Date: January 12, 2016 Unit: Relationships Within Triangles Topic: Perpendicular Bisectors Homework: Worksheet Due Monday 1/19/16 Benchmark 1/19/16 Do Now: Throwback! Using the compass and straightedge, construct a perpendicular bisector Timer Vocabulary  Concurrent – three or more lines intersect at one point  Point of concurrency – the point at which concurrent lines intersect  Circumcenter – point of concurrency of perpendicular bisectors  Circumscribed – when a circle surrounds another shape by touching all the vertices of the shape Concurrency of perpendicular Bisectors theorem  The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices How to construct perpendicular Bisector point of CONCURRENCY  Draw ∆ABC  Construct a perpendicular bisector of line AB  Construct a perpendicular bisector of line BC  Construct a perpendicular bisector of line AC  Label the point of intersection as P Example  In the diagram below, XA = What is the length of XB? Example  For ∆PQS, is PR a median, altitude or neither? Explain  Is QT a median, altitude or neither? Explain Independent Practice Timer Timer Aim: How can we use inequalities involving angles and sides of triangles? Name: Date: January 15, 2016 Unit: Relationships Within Triangles Topic: inequalities in one triangle Homework: Worksheet Due Tuesday 1/19/16 Benchmark 1/20/16 Do Now: Algebra Throwback! Solve the following inequalities: Timer Triangle Inequalities Example  A town park is triangular A landscape architect wants to place a bench at the corner with the largest angle Which two streets form the corner with the largest angle? Example  List the sides of ∆TUV in order from shortest to longest Triangle Inequality Theorem  The sum of the lengths of any two sides of a triangle is greater than the length of the third side Example: Example  Can a triangle have sides with the given lengths? Explain ft, ft, ft ft, 10 ft, 15 ft Example  Two sides of a triangle are ft and ft long What is the range of possible lengths for the third side? Independent Practice Timer Timer Aim: How can we review points of concurrency? Name: Date: January 22, 2016 Unit: Relationships Within Triangles Topic: points of Concurrency Homework: Come up with your own way to remember points of concurrency Do Now: Algebra Throwback! Solve the following equation using PEMDAS -3 * ( 5x + ) - 22 / + 3x Timer How to remember Points of Concurrency  All Of : Altitudes - Orthocenter  My Children: Medians - Centroid  Are Bringing In: Angle Bisectors - Incenter  Peanut Butter Cookies: Perpendicular Bisectors - Circumcenter Aim: How can we review points of concurrency? Name: Date: January 25, 2016 Unit: Relationships Within Triangles Topic: points of Concurrency Homework: Pass your regents Do Now: In the diagram, the perpendicular bisectors (shown with dashed segments) of MNP meet at point O—the circumcenter Find the indicated measure MO = _ PR =   MN = SP =   m∠MQO =   If OP = 2x, find x Timer Example Point S is the centroid of ∆RTW, RS = 4, VW = 6, and TV= Find the length of each segment RV =   SU =   RU =   RW =   TS =   SV =