Mr.Woods' Math Class
60866780U700U75290820103836Geometry CC00Geometry CC5108575-39370Lesson 200Lesson 260579000 00 000010160097155NYS COMMON CORE MATHEMATICS CURRICULUM00NYS COMMON CORE MATHEMATICS CURRICULUMObjective: SWBAT examine the relationships created by the medians in a triangle.Name: ____________________________________ Date: ____________ Period: _____________Lesson 2: Medians in TrianglesDo Now: The triangle below is isosceles with AB?CB. Using a compass and a straight edge, construct:The angle bisector of the vertex angle ABCThe perpendicular bisector of AC.Locate and label the midpoint of AC as point E. Draw in the median of the triangle from vertex B.center39756ABC00ABCDiscoveryThe angle bisector, median, and the perpendicular bisector are all the ______________ line in an isosceles triangle.Median in Triangles1134713359900right508000A median of a triangle is segment joining any vertex of the triangle to the midpoint of the opposite side. All triangles have ________ medians, which will intersect at one point in the interior of the triangle called the ___________.The centroid of a triangle divides the medians into a 2:1 ratio. This means that the section of the median that is closer to the vertex is twice as long as the section near the midpoint of the triangles side.-9144015819800Ex 1) Given AM is a median, CM=5x-2, and MB=3x+12, find CB.20234534063600Ex 2) Given medians FM and DN, where DM=4x-10, ME=3x+5, and FN=4x+3, find NE.Ex 3) Given medians AM, BN, and CP, where AB=24, AM=21, and CP=18, find the perimeter of ?AQP.left778600Practice: Answer each of the following questions. To be finished for homework.1. Given medians AM, BN, and CP, where AN=6.2, AP=9.5, and ?ABC is isosceles where AC=CB, find the perimeter of ?ABC.2. Given medians AM and BN of ?ABC and median PQ of ?APN. Find QA is AC=32left112147003. PM is the median of ?PQR where RM=3x-6 and MQ=5x-24. Find RQ.left68221004. In ?ABC, BX, CZ, and AY are medians. If AX=3x-9, XC=2x-4, and ZB=2x+1, what is AZ?left8919005. In ?DEF, DS, FR, and ET are medians.-5207012382500a. Find EV if VT=5b. If FR=20.1, what is the measure of VR?Closure: As shown in the diagram below, CD is a median of ?ABC.-6319613547500Which statement is not always true?(1) AD?DB(2) AC?AD(3) ∠ACD?∠CDB(4) ∠BCD?∠ACD ................
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