Question

What additional information is needed to prove that ∆LPM and ∆OPN are congruent by SAS postulate?
A. ∠P ≅ ∠P
B. ∠LPO ≅ ∠MPN
C. ∠LPM ≅ ∠OPN
D. ∠PON ≅ ∠PLM

Answer 1

Given :- What additional information is needed to prove that ∆LPM and ∆OPN are congruent by SAS postulate ?

A. ∠P ≅ ∠P

B. ∠LPO ≅ ∠MPN

C. ∠LPM ≅ ∠OPN

D. ∠PON ≅ ∠PLM

Solution :-

→ In ∆LPM and ∆OPN , we have given that,

→ LP = OP

→ MP = NP

now we know that, in order for two ∆'s to be congruent by SAS postulate we need ,

• Two corresponding sides must be equal and angle between these sides will be equal .

since two corresponding sides are equal in ∆'s . Then we can conclude that, we need angle between these sides also equal in order for two ∆'s to be congruent by SAS postulate .

therefore,

→ ∠LPM = ∠OPN .

hence,

→ ∆LPM ≅ ∆OPN { By SAS congruence rule. }

Option (C) is correct answer.

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