Using Medians and Altitudes
Presentation
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Mathematics
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9th - 10th Grade
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Practice Problem
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Medium
+1
Standards-aligned
Paige LaGrange
Used 84+ times
FREE Resource
16 Slides • 15 Questions
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Use Medians and Altitudes
Geometry
Mrs. LaGrange
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Recall: Perpendicular Bisectors
A segment, line, ray, or plane that is perpendicular to a segment at its midpoint.
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Recall: Perpendicular Bisectors
Circumcenter (Point of Concurrency of Perpendicular Bisectors): The point where three perpendicular bisectors of a triangle intersect. (Does not necessarily have to be inside the triangle.)
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Recall: Perpendicular Bisectors
The circumcenter, L, is equidistant from all three vertices of the triangle.
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Recall: Angle Bisectors of Triangles
An angle bisector of a triangle is a segment, ray, line, or plane that divides an angle into two congruent parts, called adjacent angles.
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Recall: Angle Bisectors of Triangles
Incenter (Point of concurrency of angle bisectors): The point where all three angle bisectors intersect.
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Recall: Angle Bisectors of Triangles
The incenter, I, is equidistant from all three sides of the triangle. The incenter is the center of a circle inscribes within the triangle that touches all three sides.
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
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Multiple Choice
QR is a midsegment of triangle WUV. What is the length of segment QR?
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New News: Median
A median of a triangle is a segment from a vertex to the midpoint of the opposite side.
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New News: Centroid
The point of concurrency of the medians is called the Centroid.
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New News: Centroid
Theorem: The centroid is 2/3 (two thirds) of the distance from each vertex to the midpoint of the opposite side.
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Example:
Find the length of the median.
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Example:
There are three paths through a triangular park. Each path goes from the midpoint of one edge to the opposite corner. The paths meet at point P.
Note that PC is the segment containing the vertex, so it is the segment that is 2/3 the length of the whole segment.
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Multiple Choice
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Multiple Choice
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Multiple Choice
In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
Find the length of YZ.
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Multiple Choice
Given segment AM is a median in ΔABC. Find the length of segment BC.
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New News: Altitude
An altitude of a triangle is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.
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New News: Orthocenter
The point of concurrency of the three altitudes of a triangle is called the orthocenter.
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Final note:
In an isosceles triangle, the perpendicular bisector, angle bisector, median, and altitude from the vertex angle to the base are all the same segment.
In an equilateral triangle, this is true for the special segment from any vertex.
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Multiple Choice
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Multiple Choice
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Use Medians and Altitudes
Geometry
Mrs. LaGrange
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