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How to prove if a parallelogram is a rectangle, then its diagonals are congruent, and in that case the diagonals bisect each other.
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1. "if a parallelogram is a rectangle, then its diagonals are congruent."
Let a parallelogram be a rectangle.
Consider its diagonals. Consider two triangles that have the diagonals as their sides.
Prove that the triangles are congruent.
For it, use the fact that in any parallelogram the opposite sides are congruent;
hence, the triangles have two pairs of congruent sides.
The angles between these sides are congruent, since each of these angles is the right angle.
All these argumemts combined together provide the proof.
2. "in that case the diagonals bisect each other. "
Unfortunately, this statement is not formulated unambiguously . . .
The words "in this case" remain an unanswered question: in which case?
The general relevant statement is:
In any parallelogram, the diagonals bisect each other.
See the lesson
- Properties of diagonals of parallelograms
in this site.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part of this textbook under the topic Properties of parallelograms.
H a p p y l e a r n i n g !
