To prove: The given theorem.
Explanation of Solution
Given information:
The theorem: If one diagonal of a parallelogram bisects a pair of opposite
The diagram:
Formula used:
The opposite angles of a parallelogram are congruent.
The sides of a rhombus are congruent.
ASA congruence:
If two pairs of corresponding angles and one pair of corresponding sides of two
Consider that the diagonal WY bisects the opposite angles ZWX and ZYX.
So,
Now, in triangles WXY and WZY;
WY is the common side
So, by ASA congruence;
Since,
So,
It is seen that all the sides of the parallelogram are congruent.
Hence, the theorem is proved.
Chapter 6 Solutions
Geometry, Student Edition
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