1. 7/3/20153.7: Midsegments of Triangles 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.

2. 7/3/20153.7: Midsegments of Triangles Midsegment of a Triangle Defn: A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle. A B AB is a midsegment for  XYZ. X Y Z

3. 7/3/20153.7: Midsegments of Triangles Triangle Midsegment Conjecture a. Draw ∠ ABC b. Label the midpoints of AB and AC as M and N. Draw MN. c. Determine MN and BC. Conjecture a relationship between BC and MN.

4. 7/3/20153.7: Midsegments of Triangles 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.

5. 7/3/20153.7: Midsegments of Triangles Triangle Midsegment Conjecture A midsegment of a triangle is _________ to and ______ ____ _________ of the third side.

6. 7/3/20153.7: Midsegments of Triangles 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.

7. 7/3/20153.7: Midsegments of Triangles Midsegment of a Trapezoid Defn: A midsegment of a trapezoid is a segment whose endpoints are the midpoints of the nonparallel sides.

8. 7/3/20153.7: Midsegments of Triangles 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.

9. 7/3/20153.7: Midsegments of Triangles Determine AB in the figure below. 3x - 8 8x - 2 12x + 18 A B C D

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? A) 105 B) 120 C) 135 D) 255 7/3/20153.7: Midsegments of Triangles ∠1∠1

11. 7/3/20153.7: Midsegments of Triangles Assignment pages 187-189, # 10-18 (all), 22- 40 (all) except 27