Chapter 5 Section 4 Medians and Altitudes

Sep 17, 2014

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Chapter 5 Section 4 Medians and Altitudes. Objectives. Students will be able to identify properties of medians and altitudes in triangles. Essential Understanding. A triangle’s three medians are always concurrent The altitude of a triangle are concurrent. Median of a Triangle.

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Chapter 5 Section 4 Medians and Altitudes

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Section 5 – 3 Concurrent Lines, Medians, and Altitudes

Section 5 – 3 Concurrent Lines, Medians, and Altitudes. Objectives: To identify properties of perpendicular bisectors and angle bisectors To identify properties of medians and altitudes of triangles. Concurrent :. When three or more lines intersect in one point. Point of Concurrency :.

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5-2 Medians and Altitudes N# //

5-2 Medians and Altitudes N#____ ____/____/____. Median: A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side. A. B. C. E. E1 is the median of . Find x and DF if , and . E. F.

273 views • 11 slides

Medians and altitudes

Medians and altitudes. Section 5.4. Medians of a triangle. A median of a triangle is a segment from a vertex to the midpoint of the opposite side. Altitudes of a triangle.

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Section 5.4 – Use Medians and Altitudes

Section 5.4 – Use Medians and Altitudes . HW # 22 pg. 322 #1, 4, 6, 8a, 9, 14, 33, 34, 40. Definitions . Median of a Triangle A segment from the midpoint of a side of a triangle to the opposite vertex Centroid The point where all three medians of a triangle intersect. Theorem . Example.

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Medians and Altitudes of Triangles

Medians and Altitudes of Triangles. Section 5.2 page 314-320 Guiding Question: How can a sculptor who creates mobiles use center of gravity to balance objects?. Vocabulary.

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5.4 Medians and Altitudes

5.4 Medians and Altitudes. Objectives. Use properties of medians Locate the centroid Use properties of altitudes Locate the orthocenter. Vocabulary. A. A median is a segment from a vertex of a ∆ to the midpoint of the opposite side. Every ∆ has three medians.

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Medians and Altitudes of Triangles

Medians and Altitudes of Triangles. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. Holt Geometry. Warm Up 1. What is the name of the point where the angle bisectors of a triangle intersect? Find the midpoint of the segment with the given endpoints.

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5.4 Medians and Altitudes

5.4 Medians and Altitudes. Vocabulary…. Concurrent - 3 or more lines, rays, or segments that intersect at the same point Median of a Triangle – a segment from a vertex to the midpoint of the opposite side Centroid – point of concurrency of 3 medians

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5.4  Use Medians and Altitudes

5.4  Use Medians and Altitudes. Median : segment whose endpoints are the vertex of the triangle and the midpoint of the opposite side. Median of a triangle. Centroid. Median : segment whose endpoints are the vertex of the triangle and the midpoint of the opposite side.

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5-2 Medians and Altitudes of Triangles

You identified and used perpendicular and angle bisectors in triangles. 5-2 Medians and Altitudes of Triangles. Identify and use medians in triangles. Identify and use altitudes in triangles. F. H. G. J. Median.

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Medians and Altitudes of Triangles

Medians and Altitudes of Triangles . Warm Up Lesson. Warm Up 1. What is the name of the point where the angle bisectors of a triangle intersect? Find the midpoint of the segment with the given endpoints. 2. (–1, 6) and (3, 0) 3. ( – 7, 2) and (–3, –8)

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5-4 Medians and Altitudes

5-4 Medians and Altitudes. Medians. A median of a triangle is a segment whose endpoint are a vertex and the midpoint of the opposite side. The point of concurrency of the medians is the centroid of the triangle (the “balancing” point).

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Altitudes and Medians

Altitudes and Medians. Median of A meets the mid point of BC. A. B. ( , ). x 1 +x 2 y 1 +y 2. Median. C. 2 2. m 1 m 2 = -1. Altitude. A. B. C. Altitude of A meets BC at right angles. A. Altitude from B. B. median from C. C. Altitudes and Medians.

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5-1 Bisectors, Medians, and Altitudes

5-1 Bisectors, Medians, and Altitudes. 1.) Identify and use perpendicular bisectors and angle bisectors in triangles. 2.) Identify and use medians and altitudes in triangles. 5-1 Bisectors, Medians, and Altitudes.

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Medians and Altitudes

Medians and Altitudes. 6.3. A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Every triangle has three medians, and the medians are concurrent.

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Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

Section 4.7 Medians, Altitudes, and Perpendicular Bisectors. WARM UP. Activity Part 1. Draw a triangle. Label it ∆ BOY. Measure each side of the triangle. Find and mark the MIDPOINT of each side. Activity Part 2. Draw a line connecting Point B to the MIDPOINT on the OPPOSITE SIDE.

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Section 5-3 Concurrent Lines, Medians, and Altitudes

Section 5-3 Concurrent Lines, Medians, and Altitudes. B. D. F. C. A. E. Triangle Medians A median of a triangle is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side.

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5.4 Medians and Altitudes

5.4 Medians and Altitudes. A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side. A triangle’s three medians are always concurrent. Concurrency of Medians Theorem.

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Bisectors, Medians, Altitudes

The greatest mistake you can make in life is to be continually fearing you will make one. -- Elbert Hubbard. Bisectors, Medians, Altitudes. Chapter 5 Section 1 Learning Goal: Understand and Draw the concurrent points of a Triangle. Points of Concurrency.

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Chapter 5.4 Notes: Use Medians and Altitudes

Chapter 5.4 Notes: Use Medians and Altitudes. Goal: You will use medians and altitudes of triangles. Medians A median of a triangle is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle are concurrent.

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Medians & Altitudes

Medians & Altitudes. The intersection of the medians is called the CENTROID. Theorem 5.8 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. 2x. x. C. How much is CX?. D. E. X. 13. B. A. F. C.

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5.4 – Use Medians and Altitudes

5.4 – Use Medians and Altitudes. 5.4 – Use Medians and Altitudes. As shown by the activity, a triangle will balance at a particular point. This point is the intersection of the medians of the triangle. 5.4 – Use Medians and Altitudes.

316 views • 12 slides

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Chapter 5 Section 4 Medians and Altitudes

Chapter 5 Section 4 Medians and Altitudes

Presentation Transcript

Section 5 – 3 Concurrent Lines, Medians, and Altitudes

5-2 Medians and Altitudes N#____ ____/____/____

Medians and altitudes

Section 5.4 – Use Medians and Altitudes

Medians and Altitudes of Triangles

5.4 Medians and Altitudes

Medians and Altitudes of Triangles

5.4 Medians and Altitudes

5.4  Use Medians and Altitudes

5-2 Medians and Altitudes of Triangles

Medians and Altitudes of Triangles

5-4 Medians and Altitudes

Altitudes and Medians

5-1 Bisectors, Medians, and Altitudes

Medians and Altitudes

Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

Section 5-3 Concurrent Lines, Medians, and Altitudes

5.4 Medians and Altitudes

Bisectors, Medians, Altitudes

Chapter 5.4 Notes: Use Medians and Altitudes

Medians &amp; Altitudes

5.4 – Use Medians and Altitudes

5-2 Medians and Altitudes N# //

Medians & Altitudes