Question 1195016
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This is one way to draw out the diagram to supplement the answer @greenestamps posted
<img src = "https://i.imgur.com/ygmS14C.png">
The 90 degree angle can be found using the scratch work shown at the bottom of the solution page.
We must have AD be longer than AB, otherwise the points G and H wouldn't be possible.


It then leads to this:
<img src = "https://i.imgur.com/iVdhQHi.png">
Note that if x+y = 90 and y+z = 90, then we can say x = z.
This line of thinking helps determine the missing blue and red angles.


This shows we have four congruent right triangles.
Each hypotenuse is the same, hence all four sides of this sub-figure are the same length.
This proves ABGH is a rhombus.


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Scratch Work:
<font color=blue>Angle HAB</font> + <font color=red>Angle ABG</font> = 180
<font color=blue>(Angle HAP + Angle PAB)</font> + <font color=red>(Angle ABP + Angle PBG)</font> = 180
<font color=blue>(Angle PAB + Angle PAB)</font> + <font color=red>(Angle ABP + Angle ABP)</font> = 180
<font color=blue>2*(Angle PAB)</font> + <font color=red>2*(Angle ABP)</font> = 180
2*(<font color=blue>Angle PAB</font> + <font color=red>Angle ABP</font>) = 180
<font color=blue>Angle PAB</font> + <font color=red>Angle ABP</font> = 180/2
<font color=blue>Angle PAB</font> + <font color=red>Angle ABP</font> = 90
Hence, triangle APB is a right triangle. This means all angles around point P are 90 degree angles as well.
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