Question

PL = OA and PM = OB such that PL = PM is ∆PLO ≈ ∆PMO?​

Answer 1

Answer:

Given: parllelogram ABCD circumscribe a circle

To prove: we know that pain syndrome from the extent part are equal in length.

AP=AS-------1

BP=BQ-------2

CR=CQ-------3

DR=DS-------4

Adding 1,2,3 and 4

AP+BP+CR+DR=AS+BQ+CQ+DS

AB+CD=AD+BC-------5

ABCD is a parllelogram

AB=CD

----------6

AD=BC

From 3 and 6 we get

AB+AB=AD+AD

2AB=2AD

AB=AD

If adjacent sides of parllelogram are equal then it becomes rhombus.

Hence ABCD is a Rhombus.

Answer 2

Answer:

Given

PL⊥OA , OM⊥OB and PL=PM

To Prove:

△PLO≅△PMO

Proof:

In △PLO and △PMO

∠PLO=∠PMO=90

o

PO=PO (common side)

PL=PM (given)

∴ △PLO≅△PMO by the RHS congruence property.