GEOMETRY Chapter 5 5 4 Midsegment Theorem and

GEOMETRY: Chapter 5 5. 4: Midsegment Theorem and Coordinate Proof

Theorem 5. 9 Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 295.

Ex. 1. a) Find the length of the midsegment DE if the length of AC is 12. b) Find the length of the midsegment DE if the length of AC is 19. c) Find the length of AC if the length of the midsegment DE is 7.

Ex. 2. Find x.

Ex. 3: In the diagram of an A-frame house, segment DG and segment DH are midsegments of triangle ABF. Find the length of DG and BF. Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 296.

Ex. 4: Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 296.

Write answer for example 4 here:

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.

Ex. 5: Place a square and a right triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex. Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 296.

Ex. 6: Place a rectangle in a coordinate plane. Then find the length of a diagonal and the coordinates of the midpoint M of the diagonal.

Ex. 7: Write a coordinate proof of the Midsegment Theorem for the midsegment parallel to segment OB. Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 297.

Write proof for example 7 here:

Ex. 7: Answer: Images taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 297.

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