Fͽ Figure S.26.4 shows how to draw an equilateral triangle
with a given segment as one of its sides.
To draw a hexagon, draw an equilateral triangle.
And then draw a second equilateral triangle on one
of its sides.
Do this six times to construct a hexagon.
6HHFigure S.26.5ͽ
- Draw a circle with the vertex of the angle its center. This circle
intersects the rays at two points, A and B 6HHFigure S.26.6ͽ
Draw circles each of radius AB with centers at A and B.
Let P be one of their points of intersection. Also, call the vertex of the angle O.
Then, the line OPHJJG is the angle bisector of AOB. 6HHFigure S.26.7ͽ
To see why, notice that OA = OBE\RXU¿UVWVWHSDQGAP = BP by our second step.
So, triangles OAP and OBP are similar by SSS and, therefore, #AOP BOP.
- 'UDZWKHSHUSHQGLFXODUELVHFWRURIHDFKVLGHRIWKHWULDQJOH²E\WKHPHWKRG
shown in the lesson. We know from Lesson 12 that these three line segments
meet at a common point P that is the center of the circle that passes through
each vertex of the triangle. Set one point of the compass at P and the other at
one corner of the triangle, and draw the circle of this radius with center P.
ͼ:DVLWQHFHVVDU\WRFRQVWUXFWDOOthreeSHUSHQGLFXODUELVHFWRUV"ͽ
r
rr
Figure S.26.4
A
B
Figure S.26.6
A
O P
B
Figure S.26.7
Figure S.26.5
