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The Midsegment Theorem

The Midsegment Theorem. Goal 1 Using Midsegments of Triangles. Goal 2 Using Properties of Midsegments. Using Midsegments of a Triangle. A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle This is the defn of midsegment.

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The Midsegment Theorem

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  1. The Midsegment Theorem Goal 1 Using Midsegments of Triangles. Goal 2 Using Properties of Midsegments.

  2. Using Midsegments of a Triangle A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle This is the defn of midsegment

  3. Using Midsegments of a Triangle The Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

  4. Using Midsegments of a Triangle Show that midsegment is parallel to and is half as long.

  5. Using Midsegments of a Triangle Find JK and AB

  6. Using Midsegments of a Triangle b) Why is a) What are the coordinates of Q and R? c) What is MP? What is QR?

  7. Using Midsegments of a Triangle a) In XYZ, which segment is parallel to b) Is Why? c) Find YZ and XY

  8. Using Midsegments of a Triangle Given: DE = x + 2; BC = Find DE

  9. Using Properties of Midsegments The midpoints of the sides of a triangle are S(1, 5), T(3, 3), and V(4, 6). What are the coordinates of the vertices of the triangle?

  10. Using Properties of Midsegments are midsegments in XYZ. Find the perimeter of XYZ.

  11. Using Properties of Midsegments The midpoints of the sides of a triangle are S(1, 5), T(3, 3), and V(4, 6). Find the perimeter of the triangle and the midsegment triangle. *The perimeter of a midsegment triangle is half the perimeter of the original triangle.

  12. Using Properties of Midsegments Given: X, Y, and Z are the midpoints of AB, BC, and AC respectively. AX = 2; XY = 3; BC = 9 Find the perimeter of ABC.

  13. Homework 5.4 12-18, 26-29, 36a-e, 40-52 even

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