Geometry: An Interactive Journey to Mastery

(Greg DeLong) #1

Lesson 10: Practical Applications of Similarity



  1. A line is drawn from the midpoint of the base of an isosceles triangle
    WRLWVDSH[ͼ௘6HHFigure 10.15௘ͽ
    Prove:
    D௘ͽ 7KLVOLQHELVHFWVWKHDQJOHDWB.
    E௘ͽ BMAAC.

  2. A line is drawn from the apex of an isosceles triangle to meet the base
    DWƒͼ௘6HHFigure 10.16௘ͽ
    Prove:
    D௘ͽ M is the midpoint of AC.
    E௘ͽ 7KLVOLQHELVHFWVWKHDQJOHDWB.

  3. A line is drawn from the apex of a triangle to the midpoint M of the
    opposite side. Suppose that this line turns out to be perpendicular to that
    VLGHͼ௘6HHFigure 10.17௘ͽ
    Prove that the triangle is isosceles.


B


AM C


Figure 10.15
B

AM C


Figure 10.16
B

AM C


Figure 10.17
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