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# Geometric Constructions

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USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING:

(A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE

(B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE

(C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM

********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT EACH OF THESE - YOU CAN USE DRAWINGS IF THAT IS EASIER. I HAVE TO BE ABLE TO CONSTRUCT THESE ON MY OWN AND I HAVE NEVER DONE CONSTRUCTIONS BEFORE THIS ASSIGNMENT!!!!!!! SO PLEASE, PLEASE, PLEASE BE SPECIFIC!

https://brainmass.com/math/geometry-and-topology/geometric-constructions-parallelograms-14275

## SOLUTION This solution is FREE courtesy of BrainMass!

It was very hard to convey the procedure across. However I have tried my best with figures, colours and explanations. It took quite a bit of effort to do so.

Hope this helped.

(A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE

Draw the side first.

With the angle given, mark a point above that line with your compass by placing the stationary point of the compass at one end the end of the line.

Since, in a RHOMBUS, sum of the angles adjacent sides = 180, find out the other angle by subtracting the given abgle from 180. That will be your second angle.

Place the compass stationary point on the other end of the straight line and make one more point (dot) above the drawn line.

Now you have two points (dots) above the drawn straight line, bring these two points at the same height. Since you are not asked about any length in the rhombus, just bring these two points at the same height and joint them by a straight line with your straight edge.

Alternatively,

You can also consider drawing the diagonal from the side and the angle, as shown, then cut the diagonal with same height as the height of the other side and join these two points. Then join the last side.

B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE

Compass here

Explaination : Draw a side (horizontal) with the able given draw the other side with your compass and straight edge. Draw a line (diagonal) which cuts the angle. (not necessarily in to half) Now compass positioned at the other end of the horizontal line cut the diagonal. Bring the point, at the same height as the other side and join them.

c)A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM

Explanation:

You are given the two diagonals. And angles between them.

With the two diagonals and the angles already given, the lines in blue are already there. Just draw the red lines with your straight edge, making sure that the opposite sides are parallel and cut the diagonals at some point.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!