130 Basic geometric constructions
Exercise
1.Given triangleABC, construct the equilateral trianglesBCX,CAY
andABZexternally on the sides of the triangle. JoinAX,BY,
CZ. What can you say about the intersections, lengths, and direc-
tions of these lines (segments)?
2.Show that the 90 ◦angle of a right triangle is bisected by the line
joining it to the center of the square on the hypotenuse.
3.Make a sketch to show that for two given positive quantitiesaand
b,
a+b
2
≥
√
ab≥
2 ab
a+b
.
4.Construct the following diagram.
B A
C D
5.Construct the following diagram.
B A
C D