Geometry 6.4 Midsegment Theorem mbhaub@mpsaz.org

Geometry 5.4 Midsegment Theorem Essential Question What are the properties of the midsegments of a triangle? January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 6.4 Midsegment Theorem January 2, 2019 Geometry 6.4 Midsegment Theorem

Triangle Midsegment Theorem (6.8) January 2, 2019 Geometry 5.4 Midsegment Theorem

Using the midsegment properties DE is a midsegment of ABC 12 ? 24 January 2, 2019 Geometry 5.4 Midsegment Theorem

Using the midsegment properties DE is a midsegment of ABC 5 10 ? January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Example 1: 6 ? 12 January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Example 1: 8 ? 6 4 12 January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Example 1: 10 8 6 5 ? 4 12 January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Example 1: 30 The perimeter of the outer triangle is_______. 10 8 6 5 4 12 15 The perimeter of the inner triangle is_______. January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Example 2 DE is a midsegment of ABC Solve for x. DE = ½ AB 3x + 8 17 10x + 4 34 January 2, 2019 Geometry 5.4 Midsegment Theorem

Some Old, and Important, Formulas Midpoint Distance Slope January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Coordinate Geometry On graph paper, draw RST R(0,0) S(2, 6) T(8, 0) Find M, the midpoint of RS. (1, 3) Find N, the midpoint of ST. (5, 3) Draw midsegment MN. S(2, 6) N(5, 3) M(1, 3) R(0, 0) T(8, 0) January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Coordinate Geometry Verify that MN is parallel to RT. Slope of MN S(2, 6) Slope of RT N(5, 3) M(1, 3) R(0, 0) T(8, 0) Slopes are equal: Lines are parallel. January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Coordinate Geometry Verify that MN = ½ RT. Length MN S(2, 6) Length RT N(5, 3) M(1, 3) R(0, 0) T(8, 0) MN = ½ RT January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Coordinate Geometry The theorem is verified. S(2, 6) 4 N(5, 3) M(1, 3) 8 R(0, 0) T(8, 0) January 2, 2019 Geometry 5.4 Midsegment Theorem

Geometry 5.4 Midsegment Theorem Summary A midsegment (midline) of a triangle is the segment between the midpoints of two sides. The midsegment is parallel to the third side. The midsegment is half the length of the third side. January 2, 2019 Geometry 5.4 Midsegment Theorem