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3.7: Midsegments of Triangles and Trapezoids

3.7: Midsegments of Triangles and Trapezoids. G1.2.2: Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.

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3.7: Midsegments of Triangles and Trapezoids

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  1. 3.7: Midsegments of Triangles and Trapezoids G1.2.2: Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles. G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. 3.7: Midsegments of Triangles

  2. Y B A X Z AB is a midsegment for XYZ. Midsegment of a Triangle • Defn: A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle. 3.7: Midsegments of Triangles

  3. b. Label the midpoints of AB and AC as M and N. Draw MN. Triangle Midsegment Conjecture • a. Draw ∠ABC c. Determine MN and BC. Conjecture a relationship between BC and MN. 3.7: Midsegments of Triangles

  4. Triangle Midsegment Conjecture • d. Measure ∠ABC and ∠AMN. Measure ∠ACB and ∠ANM. According to your findings, what is true about BC and MN? Justify this response. 3.7: Midsegments of Triangles

  5. Triangle Midsegment Conjecture • A midsegment of a triangle is _________ to and ______ ____ _________ of the third side. 3.7: Midsegments of Triangles

  6. In triangle ABC, m∠A=20° and m∠B= 80°. If D and E are the midpoints of AB and AC, what is m∠AED? Justify your answer with a postulate or a theorem. 3.7: Midsegments of Triangles

  7. Midsegment of a Trapezoid • Defn: A midsegment of a trapezoid is a segment whose endpoints are the midpoints of the nonparallel sides. 3.7: Midsegments of Triangles

  8. Trapezoid Midsegment Conjecture • A midsegment of a trapezoid is parallel to the bases and has a length equal to half the sum of the lengths of the bases. 3.7: Midsegments of Triangles

  9. Determine AB in the figure below. 12x + 18 B A 8x - 2 D C 3x - 8 3.7: Midsegments of Triangles

  10. A regular octagon and a regular hexagon share a common side, as shown in the diagram below. What is the measure of ∠! in the diagram? • 105 • 120 • 135 • 255 ∠1 3.7: Midsegments of Triangles

  11. Assignment • pages 187-189, • # 10-18 (all), 22- 40 (all) except 27 3.7: Midsegments of Triangles

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