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 =