Plane Geometry

Cover Plane Geometry
Plane Geometry
C a Clara Avis Hart
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Construct a triangle similar to a given triangle and having an area twice as great.
Ex. 874. Divide a given triangle into two equivalent parts by a line parallel to the base.
Ex. 875. Prove Prop. X by using 487.
Ex. 876. Draw a line parallel to the base of a triangle and cutting off a triangle that shall be equivalent to one third of the given triangle.
Ex. 877. In two similar triangles a pair of homologous sides are 10 feet and 6 feet, respectively. Find the homologous side of a similar tri- a
...ngle equivalent to their difference.
- Ex. 878. Construct an equilateral triangle whose area shall be three fourths that of a given square.
PROPOSITION XI. THEOREM \ 505. Two similar polygons are to each other as the squares of any two homologous sides.
Given two similar polygons P and P f in which a and a', b and b', etc. , are pairs of homol. Sides.
P a 2 To prove -=-.
BOOK IV 231 ARGUMENT 1. Draw all possible diagonals from any two homol. Vertices, as y and V'.
2. Then the polygons Will be divided into the same number of A ^ each to each and similarly placed, as A 1 and A I', A II and A II', etc.


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