5.5: Midsegments of a Triangle

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Presentation transcript:

5.5: Midsegments of a Triangle Objective: Define midsegment of a triangle. Use properties of midsegments to solve.

What is a Midsegment of a Triangle? Concept: What is a Midsegment of a Triangle? The midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments. The midsegment is always half the length of the side that is parallel to it..

Definition of Midsegment of a Triangle Concept: Definition of Midsegment of a Triangle The midsegment of a triangle is the segment whose endpoints are the midpoints of two sides of the triangle Midsegment Base Midsegment = ½ of Base M = ½ b

Concept: Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half of its length Midsegment x 2x

Find the length of the midsegment. Concept: Midsegment of a Triangle cont… Find the length of the midsegment. M = ½ b 23 M = ½ • 46 46 M = 23

Find the length of the base. Concept: Midsegment of a Triangle cont… Find the length of the base. M = ½ b 46 2• 46= ½ b 2• 92 92 = b

Find the length of the midsegment and the base. Concept: Midsegment of a Triangle cont… Find the length of the midsegment and the base. M = ½ b 5x - 1 = ½(6x + 10) 5•3-1 = 14 5x - 1 = 3x + 5 -3x -3x 5x - 1 2x - 1 = 5 +1 +1 6x + 10 2x = 6 2 2 6•3+10 = 28 x = 3