Geometry: An Interactive Journey to Mastery

Lesson 10: Practical Applications of Similarity

7. 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.


8. 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.


9. 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