In figure line DE is parallel to line GF ray EG and ray FG are bisectors of angle DEF and angle DFM respectively. Prove that 1. Angle DEG= half of angle EDF 2. EF=FG
Answers
Opposite rays are two rays that also both start from a common point as well as go off in exactly opposite directions and this two rays form a single straight line through the common endpoint Q.
When the two rays are opposite, the points A,Q and B are collinear.
Answer:
..(Sum of
s 180)
om (1) and (2)
ZDEF=ZEDGE GIF
From (3)
2=90
DEG ZGEF (Ray EG bisects ZDEF)
Let ZDEG=GEF=x
(1)
ZD FM=ZDF + ZFM
sures of all
(Angles addition postulate)
LDEF=x+
Form (1)
ZDEF=2
(2)
Line DE line GF
and line EF is the transversal
ZDEF LGFM (Corresponding angles)
/GFM=2x
From (2)1... (3)
4DFG /GFM (Ray FG bisects ZDFM)
ZDFG=2
From (3)]....(4)
(Angles addition postulate)
ZDFM-2r +21 From (3) and (4)
. ZDFM= 4x
(5)
DFM is an exterior angle of ADEF
.. ZDF=ZDF + ZDF
(Theorem of remote interior angles)
4x-4EDF+2r
/EDF= 4x-2r
EDF= 2/ DEG
[From (1)
Line DE line GF
(Given)
and line EG is the transversal
ZEDGE ZEDGE
.. (Alternate angles
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