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In $Δ$ ABC and $Δ$ PQR, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY.

State whether the statement regarding above information is true or false.

$Δ$ ABC $⩭ Δ$ PQR.

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True

False

answer is A.

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Detailed Solution

Given, In

Δ

ABC and

Δ

PQR, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY.
Question Image

∠ABC = 180° - ∠ABX [Since ∠ABC and ∠ABX are the angles on a straight line].

\Rightarrow

∠ABC = 180° - ∠PQY
∠PQR = 180° - ∠PQY [Since ∠PQR and ∠PQY are the angles on a straight line].

\Rightarrow

∠ABC = ∠PQR
In

△ ABC

and

△ PQR

,
∠ABC = ∠PQR (From the above calculations)
AB = PQ (Given data)
BC = QR (Given data)
So,

△ ABC ⩭ △ PQR

[By SAS congruence rule].
So, the given statement is true and the correct option is 1.

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