Draw a Parallelogram: Step-by-Step Guide

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To draw a parallelogram with given dimensions, start by noting that two sides are parallel and both diagonals bisect each other. The problem specifies one side (a) as 4cm and the sum of the diagonals (e + f) as 11cm, with an angle of 22° between side a and diagonal e. An effective method involves drawing an isosceles triangle and using perpendiculars to define key points. If side a were 8cm, it would exceed half the sum of the diagonals, making the triangle impossible to construct. Understanding these geometric relationships is crucial for accurate construction.
Redinorun
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I'd really need help with this. Thanks.

1. Homework Statement
Draw a parallelogram:
a = 4cm
e + f (diagonals) = 11cm
angle between a and e = 22°

Homework Equations


2 and 2 sides are parallel
both diagonals halve each other
(diagonal e goes from A to C)

The Attempt at a Solution


(attachment)
 

Attachments

  • Paralelogram.png
    Paralelogram.png
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Go ahead with your attempt! You have drawn the blue triangle. PRS is isosceles. Halve the side RS and draw a perpendicular at the halfpoint. It defines point P.

ehild
parallelogram.JPG
 
ehild said:
Go ahead with your attempt! You have drawn the blue triangle. PRS is isosceles. Halve the side RS and draw a perpendicular at the halfpoint. It defines point P.

ehild
View attachment 74044

Thanks, got it. You're a life saver. By the way: Why wouldn't this work if a = 8cm? Is it because a would be longer than the sum of e and b (if we take half of it as a triangle)? Or is there another explanation?
 
a can not be longer than (e+f)/2. The yellow triangle would not exist.

paral.JPG
 
ehild said:
a can not be longer than (e+f)/2. The yellow triangle would not exist.

View attachment 74049

Thank you! (I menth something like that, yes)
 

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