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11-8 Theorems Involving Midpoints

11-8 Theorems Involving Midpoints. 11-8 Theorems Involving Midpoints. There are surprising relationships among segments connecting midpoints of sides of polygons. 11-8 Theorems Involving Midpoints.

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11-8 Theorems Involving Midpoints

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  1. 11-8 Theorems Involving Midpoints

  2. 11-8 Theorems Involving Midpoints There are surprising relationships among segments connecting midpoints of sides of polygons.

  3. 11-8 Theorems Involving Midpoints Midsegment of a Trapezoid TheoremThe midsegment of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the two bases. Midsegment of a Triangle Theorem A midsegment of a triangle is parallel to and half the length of the base of the triangle.

  4. 11-8 Theorems Involving Midpoints Draw any quadrilateral in which none of the sides and none of the angles are congruent. Locate the midpoints of the sides and connect the points in order. Compare your drawing with those of the other students in your group. What seems to be true about the quadrilateral formed by the midsegments?

  5. 11-8 Theorems Involving Midpoints Consider ABC with vertices A = (6, 0), B = (–4, 0), and C = (0, 14). 1. Find the midpoints of the three sides of this triangle. 2. Show that the length of the segment connecting the midpoints of segment AB and segment BC is half the length of one of the sides of ABC.

  6. 11-8 Theorems Involving Midpoints Quadrilateral ABDF is formed by connecting the midpoints of rectangle RECT. What is the ratio of the perimeter of ABDF to the perimeter of RECT?

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