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ICSE Class 9 Answered

Prove that the bisector of any two adjacent angles of a parallelogram are at right angles 
Asked by hc4755716 | 25 Nov, 2018, 06:54: PM
answered-by-expert Expert Answer
Let ABCD is a parallelogram as shown in figure.
 
angleDAB + angleCBA = 180° (sum of interior angles.
If AE and BE are bisectors of angleDAB and angleCBA , then angleEAB + angleEBA = (1/2) ( angleDAB + angleCBA ) = 90°
Hence angleAEB = 180-90 = 90° . Hence the bisectors are at right angles
Answered by Thiyagarajan K | 26 Nov, 2018, 08:34: AM

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