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Warm up: Calculate midsegments
TODAY IN GEOMETRYβ¦ Warm up: Calculate midsegments Learning Target: 5.4 Identify the Medians of Triangles and the Centroid Independent Practice Mini Quiz β Friday! ALL HW due Friday!
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WARM UP: Complete the statement: 1. π
π β₯ 2. ππ β₯ 3. πΎπΏ β₯ 4. ππΏ β
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1. π
π β₯ 2. ππ β₯ 3. πΎπΏ β₯ 4. ππΏ β
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5. π½π
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β
6. π½π β
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πΎ π½πΏ π½πΎ π
π π
π πΎπ π
π πΏ π½ π πΎπ
ππ πΏπ π
π
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MEDIAN OF A TRIANGLE: A segment from a vertex to the midpoint of the opposite side.
Find the midpoint on one segment. Draw a line from the opposite vertex through the midpoint. vertex median midpoint
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The three medians of a triangle are concurrent
The three medians of a triangle are concurrent. The point of concurrency is called the CENTROID and falls inside the circle. The centroid is the balancing point of a triangle. Find the medians for each side of the triangle. CENTRIOD
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A different way to think about this:
CONCURRENCY OF MEDIANS: The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. π΄π= 2 3 π΄π΅ π΄ A different way to think about this: π΄π is twice as long as π΅π OR π΅π is half of π΄π ππ π π π΅ CENTRIOD
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PRACTICE: π is the centroid of β³π΄π·πΈ, πΆπΈ=27
π΅ πΆ πΈ πΉ 1. πΉπΈ= 2. πΆπ= 3. ππΈ= 4. πΉπ= 5. πΉπ·= 6. π΄πΈ= π΄πΉ=12 12 1 3 πΆπΈ=9 2 3 πΆπΈ=18 1 2 π·π=3 6 πΉπ+ππ·=9 2π΄πΉ=24
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PRACTICE: πΊ is the centroid of β³π΄π΅πΆ. Find x.
1. πΆπΊ=3π₯+7 πππ πΆπΈ=6π₯ πΆπΊ= 2 3 πΆπΈ 3π₯+7= 2 3 (6π₯) 3π₯+7=4π₯ β 3π₯ β 3π₯ π=π 2. πΉπΊ=π₯+8 πππ π΄πΉ=9π₯β6 πΉπΊ= 1 3 π΄πΉ π₯+8= 1 3 (9π₯β6) π₯+8=3π₯β2 β π₯ β π₯ 8=2π₯β2 10=2π₯ π΄ π΅ πΊ π· πΈ πΆ πΉ π=π
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PRACTICE: Find the midpoint π of π΄πΈ then draw the median
PRACTICE: Find the midpoint π of π΄πΈ then draw the median. Use the median π΄π to find the coordinates of the centroid. Midpoint Formula π( π₯ 1 + π₯ 2 2 , π¦ 1 + π¦ 2 2 ) Substitute Values , 7+1 2 Add and Divide (7, 4) Connect the midpoint π to vertex πΆ Centroid is πΆπ= =6 Count 6 units down from the vertex πΆ Centroid is (7, 7) πΆ(7, 13) π (7, 7) π΄(3, 7) π(7 4) πΈ(11, 1)
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HOMEWORK #2: Pg. 322: 3-11, 33-35 If finished, work on other assignments: HW #1: Pg. 298: 3-15, 24-27
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