Answer :

__Given:-__ AB=AC and ABC is isosceles triangle

∠ QAD=∠ DAC

CD||BA

__Formula used:-__ sum of angles of triangle is 180°

__Solution:__-

As Δ ABC is a isosceles triangle

∠ ABC=∠ ACB

∠ ABC+∠ ACB+∠ CAB=180°

2∠ ACB+∠ CAB=180°

*As BAQ is a straight line

∠ CAB+∠ DAC+∠ QAD=180°

*∠ QAD=∠ DAC [Given]

∠ CAB=180° - 2∠ DAC

Putting value of ∠ CAB in above equation 1

2∠ ACB+180° - 2∠ DAC=180°

2∠ ACB =2∠ DAC

∠ ACB =∠ DAC

If;

There is ∠ ACB =∠ DAC and AC is the transverse

∴ these are equal by alternate angles

And AD||BC

In ABCD

If;

AD||BC & CD||BA

If both pair of sides of quadrilateral are parallel

Then the quadrilateral is parallelogram

__Conclusion:-__

ABCD is a parallelogram

And ∠DAC = ∠BCA

Rate this question :

In <span lang="ENAP- Mathematics

ABCD is a paralleAP- Mathematics

In the adjacent fAP- Mathematics

ABCD is a paralleAP- Mathematics

In the adjacent fAP- Mathematics

ABC is an isoscelAP- Mathematics

The opposite anglAP- Mathematics

Show that the diaAP- Mathematics

Find the measure AP- Mathematics

In the adjacent fAP- Mathematics