Lesson 5.3.notebook November 28, 2012
Warm‐up
Use the figure below for problems 1 and 2. 1. Find BD
2. Find CA
Use the figure below for problem 3. 3. Find the perimeter of quadrilateral ABCG
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Page 267 Homework Answers
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Proofs Page 267
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Proofs Page 267
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Lesson 5.3 ‐ Concurrent Lines, Medians, and Altudes
Vocabulary Concurrent lines are three or more lines that intersect in one point.
The point of concurrency is the point at which concurrent lines intersect.
A circle is circumscribed about a polygon when the verces of the polygon are on the circle
The circumcenter of a triangle is the point of concurrency of the perpendicular bisectors of a triangle.
A median of a triangle is a segment whose endpoints are on a vertex and the midpoint of the opposite side.
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Vocabulary
A circle is inscribed in a polygon if the sides of the polygon are equidistant from the incenter of the polygon.
The incenter of a triangle is the point of concurrency of the angle bisectors of a triangle.
The altude of a triangle is the perpendicular segment from a vertex to a line containing the opposite side.
The centroid of a triangle is the point of concurrency of the medians.
The orthocenter of a triangle is the point of intersecon of the lines containing the altudes of the triangles.
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Vocabulary and Key Concepts
Theorem 5.6 The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the verces.
Theorem 5.7 The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides.
Theorem 5.8
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
Theorem 5.9
The lines that contain the altudes of a triangle are concurrent.
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Ex 1: Find the center of the circle that circumscribes ΔXYZ
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Ex 2: M is the centroid of ΔWOR, and WM = 16. Find WX.
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Ex 3: In ΔABC, centriod D is on median AM. AD = x + 4 and DM = 2x ‐ 6. Find AM.
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Homework: Page 275 #1‐9, 11‐16, 19‐22, 27‐30, 37‐39
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