Question

in the figure of CA and DB are perpendicular to CD and CA=DB, prove that PA=PB

Answer 1

Answer:

Step-by-step explanation:

In tri(ACP) & tri(PDB)

=APC=DPB(VERTICALLY OPPOSITE)

ACP=BDP(EACH 90)

CA=BD (GIVEN)

therefore triACP=triPDB(by AAS rule)

PA=PB(C. P. C. T)

hence proved

Answer 2

PA = PB

PA = PB Hence, Proved

GIVEN

CA⏊CD

DB ⏊ CD

TO PROVE

PA = PB

SOLUTION

We can simply solve the above problem as follows;

In ΔACP and ΔPDB

∠PCA = ∠PDB = 90°

AC = DB (Given)

∠APC = ∠DPB (Vertically opposite angle)

By A-S-A congruency

ΔACP ≈ ΔPDB

We know that,

Parts of congruent triangle are congruent.

PA = PB

PA = PB Hence, Proved.

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