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# Chapter6 - More About Triangles 6.1 Medians 6.2 Altitudes...

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More About Triangles § 6.1 6.1 Medians Medians § 6.4 6.4 Isosceles Triangles Isosceles Triangles § 6.3 Angle Bisectors of Triangles Angle Bisectors of Triangles § 6.2 6.2 Altitudes and Perpendicular Bisectors Altitudes and Perpendicular Bisectors § 6.6 6.6 The Pythagorean Theorem The Pythagorean Theorem § 6.5 6.5 Right Triangles Right Triangles § 6.7 Distance on the Coordinate Plane Distance on the Coordinate Plane

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Medians Yo u will le arn to   ide ntify and c o ns truc t m e dians   in triang le s   1) ______ 2) _______ 3)  _________ m e di an c e ntro id c o nc urr e nt
Medians In a triangle, a median is a segment that joins a ______ of the triangle and the ________ of the side __________________. ve rt e x m idpo i nt o ppo s ite  that  ve rte x C B A D E F BE median AD median CF median c e ntro id The medians of ΔABC, AD, BE, and CF, intersect at a common point called the ________. When three or more lines or segments meet at the same point, the lines are __________. c o nc urr e nt

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Medians There is a special relationship between the length of the segment from the vertex to the centroid D C B A E F and the length of the segment from the centroid to the midpoint .
Medians Theorem 6 - 1 The length of the segment from the vertex to the centroid is _____ the length of the segment from the centroid to the midpoint. twic e x 2x When three or more lines or segments meet at the same point, the lines are __________. c o nc urre nt

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Medians D C B A E F . of medians are and , , ABC CF BE AD ? 9 2 and , 1 5 , 3 4 CE if of measure the is What + = - = + = x EA x DB x CD C D =  14

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Altitudes and Perpendicular Bisectors Yo u will le arn to  ide ntify and c o ns truc t _______ and __________________ in triang le s .  1) ______ 2) __________________ altitude s pe rpe ndic ular bis e c to rs altitude pe rpe ndic ular bis e c to r
Altitudes and Perpendicular Bisectors In geometry, an altitude of a triangle is a ____________ segment with one endpoint at a ______ and the other endpoint on the side _______ that vertex. pe rpe ndic ular ve rte x o ppo s ite D The altitude AD is perpendicular to side BC. C A B

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Altitudes and Perpendicular Bisectors C A B Constructing an altitude of a triangle 1) Draw a triangle like ΔABC 2) Place the compass point on B and draw an arc that intersects side AC in two points. Label the points of intersection D and E. 3) Place the compass point at D and draw an arc below AC. Using the same compass setting, place the compass point on E and draw an arc to intersect the one drawn. 4) Use a straightedge to align the vertex B and the point where the two arcs intersect. Draw a segment from the vertex B to side AC. Label the point of intersection F. D E
Altitudes and Perpendicular Bisectors An altitude of a triangle may not always lie inside the triangle.

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Chapter6 - More About Triangles 6.1 Medians 6.2 Altitudes...

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