0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Prove that the bisectors of opposite angles of a parallelogram are parallel.

Solution
Verified by Toppr

ABCD is a parallelogram, the bisector of ADC and BCD meet at point E and the bisectors of BCD and ABC meet at F. We have to prove that the CED=90o and CFG=90o. This way we will be able to prove that DE and CE intersect at right angles and BG and ED are parallel. This way we will be able to prove that DE and CE intersect at right angles and BG and ED are parallel.
ADC+BCD=180o [sum of adjacent angles of a parallelogram]
ADC2+BCD2=90o
EDC+ECD=90o
In ECD sum of angle =180o
EDC+ECD+CED=180o
CED=90o
Hence, the first condition is proved that in a parallelogram the bisectors of angles intersect at 90o
In ECD, sum of angles =180o
EDC+ECD+CED=180o
CED=90o
Hence, the first condition is proved that in a parallelogram, the bisectors of angle intersect at 90o
Similarly taking ABCF,BFC=90o
BFC+CFG=180o
CFG=90o
DE||BG
Hence proved

946349_194919_ans_4969a765e64f48098a78d25e1c2be849.png

Was this answer helpful?
0
Similar Questions
Q1
Prove that the bisectors of opposite angles of a parallelogram are parallel.
View Solution
Q2
Prove that the bisectors of two opposite angles of a parallelogram are parallel.
View Solution
Q3
In case of a parallelogram prove that :
(i) the bisector of any two adjacent angles intersect at 90o.
(ii) the bisector of opposite angle are parallel to each other.
View Solution
Q4
The bisectors of opposite angles of a parallelogram are parallel.
View Solution
Q5

Prove that the opposite angles of a parallelogram are equal.

View Solution