What can be said about this quadrilateral ?
Geometry
Level
pending
ABCD is a rectangle with length of AB and BC equal to 6 and 8 respectively. H, E, G and F are mid points of the sides AB,AD,DC and BC respectively. What can be said about the quadrilateral HEGF.
It is a rectangle.
It is a square
All four sides are equal but it is not a square
All four sides have distinct length
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
AH = 3 and AE = 5 ; By the Pythagoras theorem HE = 5; Similarly it can be easily seen that all the sides EG, FG and HF are also equal to 5. Angle HEG is 180 - 2* Angle AEH. Angle AEH is arctan(3/4) = 36.86989765 degrees. So angle HEG = 106.262 degrees, angle EHF is equal to 73.738 degrees. Hence the quadrilateral HEGF is a Rhombus.