Question

please answer the questions step by step instructions​

Answer 1

$\large{\underline{\underline{\bold{\bf{Answer:}}}}}$

To Prove : ABCD is a parallelogram.

Proof:

∠WCA = ∠CAZ ( alternate interior angles)

$\frac{1}{2}$∠WCA = $\frac{1}{2}$∠CAZ

∠DCA = ∠CAB (given CD bisects ∠WCA and AB bisects ∠ CAZ)

Now, with AC as transversal, ∠DCA = ∠CAB (alternate interior)

So, DC ║ AB

Similarly,

∠YAC = ∠ACX ( alternate interior angles)

$\frac{1}{2}$∠YAK = $\frac{1}{2}$∠ACX

∠DAC = ∠ACB (given AD bisects ∠YAC and BC bisects ∠ ACX)

Now, with AC as transversal, ∠DAC = ∠ACB (alternate interior)

So, AD ║ BC

now, DC║AB, AD║BC

therefore, ABCD is a parallelogram

hence, proved

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