Construct a square with diagonal 6 cm without using a protractor.
Draw a line segment of 6 cm as the diagonal. Find its midpoint. Through this midpoint, draw a perpendicular line segment of 6 cm (the other diagonal). The four endpoints of these perpendicular, bisecting diagonals form the vertices of the square. Join these points to complete the square.
Explanation
The chapter establishes in Deduction 5 that the diagonals of a square are equal and bisect each other at right angles. To construct a square with diagonal 6 cm: (1) Draw diagonal AC = 6 cm. (2) Find midpoint O. (3) Draw diagonal BD perpendicular to AC at O, also of length 6 cm. (4) Join A, B, C, D to form the square. No protractor is needed since perpendicular lines can be drawn using a compass and ruler.
Solution Steps
Step 1: Draw a line segment AC = 6 cm.
Step 2: Find the midpoint O of AC using compass construction.
Step 3: At point O, construct a perpendicular line using compass.
Step 4: Mark points B and D on this perpendicular such that OB = OD = 3 cm.
Step 5: Join points A, B, C, D in order to form the square.