Question

By using which of the following conditions, a unique triangle cannot be constructed?

• A.
  
  Two sides and included angle are given
• B.
  Three sides are given
• C.
  Two angles are given
• D.
  
  In a right triangle, hypotenuse and one side are given

Answer 1

The correct option is C

Two angles are given
The minimum number of independent measurements required to construct a triangle is 3.
Now consider a triangle PQR.
Case 1- Two sides PQ and QR and base angle ∠PQR is given then, ΔPQR can be easily constructed.
Case 2- Three sides PQ, QR and RP are given then, ΔPQR can be constructed.
Case 3- If PQR is right-angled triangle where ∠PQR = 90°, hypotenuse PR and one side QR is given then, ΔPQR can be constructed.
Case 4- When only two angles ∠PQR and ∠QPR are given then, it is not possible to construct the triangle.
Hence, the correct answer is option (c).