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5.1 Midsegment Theorem and Coordinate Proof

5.1 Midsegment Theorem and Coordinate Proof. Hubarth Geometry. Midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has three midsegments. B. P. M. C. A. N. Midsegment Theorem

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5.1 Midsegment Theorem and Coordinate Proof

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  1. 5.1 Midsegment Theorem and Coordinate Proof Hubarth Geometry

  2. Midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has three midsegments. B P M C A N Midsegment Theorem The segments connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. C D E A B ll

  3. Triangles are used for strength in roof trusses. In the diagram, UVand VWare midsegmentsof Find UVand RS. 1 1 2 2 RT ( 90 in.) = 45 in. = = UV VW ( 57 in.) 2 2 = 114 in. = = RS Ex 1 Use the Midsegment Theorem to Find Lengths

  4. In the kaleidoscope image, AEBEand AD CD. Show that CB ll DE. Ex 2 Use the Midsegment Theorem ll

  5. b. a. Notice that you need to use three different variables. Let hrepresent the length and krepresent the width. A rectangle A scalene triangle a. b. Ex 3 Place a Figure in a Coordinate Plane Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex. It is easy to find lengths of horizontal and vertical segments and distances from (0, 0), so place one vertex at the origin and one or more sides on an axis.

  6. = = = = k 2 k k 2 2 = 0 + k , k+0 M( ) M( , ) 2 2 2 2 2 2 2 2 2 k + (– k) 2k k + k (k–0) + (0–k) Ex 4 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. Place PQOwith the right angle at the origin. Let the length of the legs be k. Then the vertices are located at P(0, k), Q(k, 0), andO(0, 0). Use the Distance Formula to find PQ. PQ = Use the Midpoint Formula to find the midpoint Mof the hypotenuse.

  7. Practice 1. Draw and name the third midsegment in the diagram. UW 2. From the diagram suppose the distance UWis 81 inches. Find VS. 81 in. Find the value of the variable. q 3. 4. 8 14 11 P 8 11 16

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