ESSENTIAL QUESTION -How do you identify medians in triangles.

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Presentation transcript:

ESSENTIAL QUESTION -How do you identify medians in triangles.

median of a triangle a segment from a vertex to the midpoint of the opposite side.

Copy the triangle and draw a median to the base. Checkpoint Draw a Median Copy the triangle and draw a median to the base. 1. ANSWER Sample answer: 2. ANSWER Sample answer: 3. ANSWER Sample answer:

Centroid of a triangle The point where all three medians of the triangle intersect.

Centroid Theorem Intersection of Medians of a Triangle The distance from the vertex to the centroid is two thirds of the distance from each vertex to the midpoint of the opposite side =2/3(entire segment)

E is the centroid of ∆ABC and DA = 27. Find EA and DE. Example 2 Use the Centroid of a Triangle E is the centroid of ∆ABC and DA = 27. Find EA and DE. SOLUTION Using Theorem 4.9, you know that EA = DA = (27) = 18. 2 3 DA = DE + EA 27 = DE + 18 – 18 = – 18 9 = DE ANSWER EA has a length of 18 and DE has a length of 9. 6

P is the centroid of ∆QRS and RP = 10. Find the length of RT. Example 3 Use the Centroid of a Triangle P is the centroid of ∆QRS and RP = 10. Find the length of RT. SOLUTION 2 3 RP = RT 2 3 10 = RT = 3 2 (10) RT 15 = RT ANSWER The median RT has a length of 15. 7

The centroid of the triangle is shown. Find the lengths. Checkpoint Use the Centroid of a Triangle The centroid of the triangle is shown. Find the lengths. 4. Find BE and ED, given BD = 24. 5. Find JG and KG, given JK = 4. 6. Find PQ and PN, given QN = 20.

The centroid of the triangle is shown. Find the lengths. Checkpoint Use the Centroid of a Triangle The centroid of the triangle is shown. Find the lengths. 4. Find BE and ED, given BD = 24. 5. Find JG and KG, given JK = 4. ANSWER BE = 16; ED = 8 ANSWER JG = 12; KG = 8 6. Find PQ and PN, given QN = 20. ANSWER PQ = 10; PN = 30

Classify the triangle as right, acute, or obtuse. 1. 2. 3.

Classify the triangle as right, acute, or obtuse. 1. ANSWER acute 2. ANSWER right 3. ANSWER obtuse

4. Madeline makes this picture frame with a diagonal cross piece attached to the back for support. Can you tell from the dimensions whether or not the corners of the frame are right angles? Explain. Yes, the frame corners are right angles because 362 + 152 = 392. ANSWER

Hw Practice 4.6A