5.1%20

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5.1 Midsegment Theorem and Coordinate Proof

• A midsegment of a triangle is a segment that
  connects the midpoints of two sides of the
  triangle. Every triangle has three midsegments.
  
• The midsegments of Triangle ABC
• at the right are
• Segment MP, Segment MN,
• and Segment NP.

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5.1 Midsegment Theorem and Coordinate Proof
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5.1 Midsegment Theorem and Coordinate Proof

• Example 1
• Triangles are used for strength in roof trusses.
  In the diagram, Segment UV and Segment VW are
  midsegments of Triangle RST. Find UV and RS.

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5.1 Midsegment Theorem and Coordinate Proof

• Example 2
• In the diagram of an A-frame house, Segment DG
  and Segment DH are midsegments of Triangle ABF.
• Find DG and BF.

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5.1 Midsegment Theorem and Coordinate Proof

• A coordinate proof involves placing geometric
  figures in a coordinate plane. When you use
  variables to represent the coordinates of a
  figure in a coordinate proof, the results are
  true for all figures of that type.

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5.1 Midsegment Theorem and Coordinate Proof

• Example 4
• Place each figure in a coordinate plane in a way
  that is convenient for finding side lengths.
  Assign coordinates to each vertex.
• A rectangle b. A scalene triangle
• c. An isosceles triangle d. A square

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5.1 Midsegment Theorem and Coordinate Proof

• Example 5
• Place an isosceles right triangle in a coordinate
  plane. Then find the length of the hypotenuse
  and the coordinates of its midpoint M.

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5.1 Midsegment Theorem and Coordinate Proof

• Example 5

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5.1 Midsegment Theorem and Coordinate Proof

• Example 5