two parallel line l and m intersect by tansevasal p shwo that the quadrilateral formed by the bisector of interior angle is rectangle
Answers
Answer :-
Given :
- line m and l are parallel and
transversal p intersect.
To prove:
- ABCD is rectangle.
Proof:
- We know that a rectangle is a parallelogram with one angle 90°
First we will prove ABCD is a parallelogram,
For m & transversalp
PAC = 2 ACR Alternate angles)
SOPAC LACE
i.e., BAC ACD (Given A bisects PAC & CO bisects ACR
For lines AB and DC with AC as transversal
BAC & ACD are alternate angles,
and they are equal
So, AB DC
Similarly,
torlines BC & AD, with AC as transversal
BAC & ACD are alternate angles, and they are equal
BC IAD
Now, In ABCD,
AB DC & BC AD
As both pairs of opposite sides are parallel,
ABCD is a parallelogram.
Also for line?
PAC+ 2 CAS 180 (Linear Pair)
Multiplying both sides by har
MACCAS 180
Z BAC + 2 CAD-90 CAB is bisector of PAC
&.BC bisector of CAS)
BAD = 90°
So, ABCD is a parallelogram in which one angle is 90°
ABCD is a rectangle.
mark as brainliest answer.
Answer:
Answer :-
Given :
line m and l are parallel and
transversal p intersect.
To prove:
ABCD is rectangle.
Proof:
We know that a rectangle is a parallelogram with one angle 90°
First we will prove ABCD is a parallelogram,
For m & transversalp
PAC = 2 ACR Alternate angles)
SOPAC LACE
i.e., BAC ACD (Given A bisects PAC & CO bisects ACR
For lines AB and DC with AC as transversal
BAC & ACD are alternate angles,
and they are equal
So, AB DC
Similarly,
torlines BC & AD, with AC as transversal
BAC & ACD are alternate angles, and they are equal
BC IAD
Now, In ABCD,
AB DC & BC AD
As both pairs of opposite sides are parallel,
ABCD is a parallelogram.
Also for line?
PAC+ 2 CAS 180 (Linear Pair)
Multiplying both sides by har
MACCAS 180
Z BAC + 2 CAD-90 CAB is bisector of PAC
&.BC bisector of CAS)
BAD = 90°
So, ABCD is a parallelogram in which one angle is 90°
ABCD is a rectangle.
mark as brainliest answer.
Step-by-step explanation: