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Byju's Answer
Standard IX
Mathematics
Angle Sum Property of a Polygon
In the figure...
Question
In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?
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Solution
Given that,
ABCP is a parallelogram with OP || BC.
We know that,
If a line is drawn through the mid-point of a side of a triangle parallel to the second side, it will bisect the third side.
Since P is the mid-point of CD and OP || BC, O is the mid point of BD by converse of mid-point theorem.
Hence,
O
B
=
1
2
B
D
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Q.
In the given figure, AB = AC and CP || BA and AP is the bisector of exterior ∠CAD of ΔABC. Prove that (i) ∠PAC = ∠BCA (ii) ABCP is a parallelogram.