In a , < PQR = < PRQ = 45o. which of the following statements is/are correct? i. \(\bigtriangleup\)PQR is an equalateral triangle ii. \(\bigtriangleup\)PQR is an isosceles triangle iii. \(\bigtriangleup\)PQR is a right-angled triangle
- ii only
- i and ii only
-
ii and iii only
- i and ii only
The correct answer is: C
Explanation
Statement ii: △PQR is an isosceles triangle.
This statement is correct. Since two angles are equal (45º ), the triangle must have at least two equal sides.
Statement iii: △PQR is a right-angled triangle.
This statement is correct. The sum of the angles in a triangle is 180º
Therefore, the third angle ∠QRP can be calculated as: ∠QRP = 180º −(45º + 45º ) = 90º