In figure, $C B = A D$ and $A B = C D$ . Can we say $∠ A B C$ and $∠ A D C$ are equal? Why?

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Solution

In $Δ A B C$ and $Δ A D C$
$A B = D C$
$A D = C B$
and $A C = A C$
$Δ A B C = Δ A D C$ (by SSS congruency property)
So, $∠ A B C = ∠ A D C$ (by c.p.c.t)
Hence proved.

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In figure, CB=AD and AB=CD. Can we say ∠ABC and ∠ADC are equal? Why?

In ΔABC and ΔADCAB=DCAD=CBand AC=ACΔABC=ΔADC (by SSS congruency property)So, ∠ABC=∠ADC (by c.p.c.t)Hence proved.

In figure, $C B = A D$ and $A B = C D$ . Can we say $∠ A B C$ and $∠ A D C$ are equal? Why?

In $Δ A B C$ and $Δ A D C$
$A B = D C$
$A D = C B$
and $A C = A C$
$Δ A B C = Δ A D C$ (by SSS congruency property)
So, $∠ A B C = ∠ A D C$ (by c.p.c.t)
Hence proved.