section 5.1 midsegment theorem and coordinate proof

Section 5.1 Midsegment Theorem and Coordinate Proof

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Section 5.1

Midsegment Theorem and Coordinate Proof

Homework

• Pg 298 #3-11, 36 (prove 36)

Page 3: Section 5.1 Midsegment Theorem and Coordinate Proof

Vocabulary

• Midsegment of a triangle – is a segment that connects the midpoints of two sides of a triangle.

• Coordinate Proof – placing geometric figures in a coordinate grid, then using variables to represent coordinates.

Page 4: Section 5.1 Midsegment Theorem and Coordinate Proof

Theorem 5.1: Midsegment Theorem

DE AC and DE=12

The segment connecting themidpoints of two sides of atriangle is parallel to thethird side and is half as longas that side

D E

A C

Page 5: Section 5.1 Midsegment Theorem and Coordinate Proof

Apply variable coordinates

Place an isosceles right triangle in a coordinate plane. Then find the length of the hypotenuse and the coordinates of its midpoint M.

Page 6: Section 5.1 Midsegment Theorem and Coordinate Proof

Prove the Midsegment Theorem

GIVEN : DE is a midsegment of OBC.

PROVE :DE OC and DE = OC12

Write a coordinate proof of the Midsegment Theorem for one midsegment.

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