Fill in the blanks:
(i) The sum of any two sides of a triangle is ...... the third side.
(ii) The sum of the angles of a triangle is ...... .
(iii) A triangle has ...... vertices and ...... sides.
(iv) All angles of a scalene triangle are ...... .
(v) The medians of a triangle are ...... .
Answer
(i) The sum of any two sides of a triangle is greater than the third side.
(ii) The sum of the angles of a triangle is 180°.
(iii) A triangle has 3 vertices and 3 sides.
(iv) All angles of a scalene triangle are unequal.
(v) The medians of a triangle are concurrent.
Write (T) for true and (F) for false for each of the following statements:
(i) A triangle can have two obtuse angles. ......
(ii) A triangle can have two acute angles. ......
(iii) A triangle can have two right angles. ......
(iv) The sum of any two angles of a triangle is greater than the third angle. ......
(v) In a right triangle, the sum of the two acute angles is 90°. ......
Answer
(i) F — two obtuse angles would each be more than 90°, so their sum alone would exceed 180°.
(ii) T — every triangle has at least two acute angles.
(iii) F — two right angles would add up to 180°, leaving nothing for the third angle.
(iv) F — this is not always true; for example, in a triangle with angles 30°, 30° and 120°, the sum 30° + 30° = 60° is less than 120°.
(v) T — the third angle is 90°, so the two acute angles add up to 90°.