Question

in the given figure, the point p bosectsAB and DC.prove that∆APC=~∆BPD​

Answer 1

Answer:Δ A P C ≅ Δ B DPD    

Hence proved.

Step-by-step explanation:

Given:

In the figure, the point P bisects AB and DC that means point P is the angle bisector of AB and DC.

PA=PB            

To prove,

ΔAPD≅ΔBPD

PA=PB                           [Given]

∠APC=∠BOD                [vertically opposite ange]

PD=PC                            [adjacent sides]

ΔAPD≅ΔBPD    [SAS congruency]

Hence proved.

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Answer 2

To prove:-

• ∆APC ≌ ∆BPD

Solution:-

We know, If two lines bisect they divides in equal part.

So,

AP = BP ------------(i)

CP = DP ------------(ii)

We also know that,

If two lines bisect or intersect there Vertical angles are equal. This statement also known as Vertically opposite angle.

Therefore,

∠APC = ∠DPB

In ∆APC and ∆BPD

➨ AP = BP [By equation (i)]

➨ ∠APC = ∠DPB ( Vertically opposite angle)

➨ CP = DP [By equation (ii)]

So,

By SAS congruency ,

∆APC ≌ ∆BPD

Hence, Proved that,

∆APC ≌ ∆BPD