Rectangle-ception

Geometry Level 2

What figure do you get when you connect up the midpoints of a rectangle?

The midpoint of a line segment is the middle of the line segment.

Rectangle Rhombus Square Trapezoid

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Nikkhil Kalia by Nikkhil Kalia , 22, India

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5 solutions

Aji Karunakaran
May 22, 2014

Distance between any two adjacent midpoints of a rectangle is constant. When those points are joined, it gives a flat shape with four equal straight sides, which is a Rhombus.

9 Helpful 0 Interesting 0 Brilliant 0 Confused

because I used my math skills

Bill Le - 7 years ago

my mistake

Amritesh Kashyap - 7 years ago

Actually rhombus is also a square and rectangle is also a square just that they have specific name called as rectangle and rhombus right? hahaa

Zack Yeung - 5 years, 10 months ago

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A square is a rhombus and a square is a rectangle. It's not true that a rhombus is a square or a rectangle is a square.

Ivan Koswara - 5 years, 10 months ago
Clara Maxcy
May 22, 2014

Given Rectangle ABCD. Segment AB congruent CD. (Properties of Rectangle) Segment AD congruent BC. (Properties of Rectangle) Designate point Q midpoint of AB; point R midpoint of BC; point S midpoint of CD; point T midpoint of AD. Therefore: Segments AQ congruent to QB congruent to CS congruent to SD; segments BR congruent to RC congruent to AT congruent to TD: Midpoint creates two equal segments; Draw line segments QR, RS, ST, TQ to create four congruent triangles: QBR, RCS, SDT; TAQ: SAS congruency Segments QR, RS, ST, TQ are congruent: SAS congruency. Segments QR, ST are parallel, segments RS and TQ are parallel: SAS congruency and translation. Opposite Angles QRS, STQ are congruent: linear angles congruency. Opposite angles RST, TQR are congruent: linear angles congruency. Therefore, figure QRST is a rhombus: properties of a rhombus.

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By joining the mid points of a rectangle we get a figure having four equal sides but no angle is right angle, called a Rhombus.

Lubna Shahid - 7 years ago
Hadia Qadir
Jul 26, 2015

By joining the mid point of a rectangular we get a figure having four equal side but no angle is a right angle . that is called Rhombus

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Roshan Cheereth
May 25, 2014

The lines joining the midpoints of adjacent sides a rectangle are always parallel to the line joining the other two midpoints irrespective of the lengths of the sides of the rectangle and will always turn out to be a rhombus

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Simone Sibone
May 24, 2014

one can solve this problem using mid point theorem and congruency, the figure obtained will be that of a Rhombus.

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