Question

1) In DPQR, PQ = 5 cm ÐPQR = 45 and ÐRPQ = 45 . Which criterion can be used to

construct DPQR?​

Answer 1

Given :- In ∆PQR, PQ = 5 cm . ∠PQR = 45° , ∠RPQ = 45° .

To Find :- Which criterion can be used to construct ∆PQR ?

Answer :-

using angle sum property of ∆ , we get,

→ ∠PQR + ∠RPQ + ∠PRQ = 180°

→ 45° + 45° + ∠PRQ = 180°

→ 90° + ∠PRQ = 180°

→ ∠PRQ = 180° - 90°

→ ∠PRQ = 90° .

also,

→ ∠PQR = ∠RPQ

then,

→ PR = RQ { Angle opposite to equal sides are equal in length .}

therefore, we can conclude that, ∆PRQ is a right angle isosceles triangle with hypotenuse PR as 5 cm .

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