How are the points M,N,P and Q chosen?
Are they at the same distance from the adjacent vertex?
Can some one please help me figure the angles out? sorry I can't copy and paste the figures...
The 17in x 17in square below is given. We have chosen 4 points M, N, P, and Q one on each of its sides as shown in the figure and joint them to obtain a new four sided figure in red.
Show that the figure in red is also a square (Which means has all four angles 90º and all four sides equal). What is the angle QMN or the angle MQP? Justify your answer Why 90º? Not all the 4 sided figures with equal 4 sides are squares!
3 answers
yes it is a smaller box inside another box
I am labeling as follows starting at the lower left of the big box and going clockwise:
A M B N C P D Q
AM = AQ
so AMQ is isosceles
<A is right
so
<AMQ is 45
same system to get <BMN = 45
and congruent to AMQ
AB is straight (180)
therefore <NMQ = 180-45-45 = 90
MQ=MN because corresponding sides of congruent triangles
etc
A M B N C P D Q
AM = AQ
so AMQ is isosceles
<A is right
so
<AMQ is 45
same system to get <BMN = 45
and congruent to AMQ
AB is straight (180)
therefore <NMQ = 180-45-45 = 90
MQ=MN because corresponding sides of congruent triangles
etc
1 answer