Question

Fill in the blanks to make the following statements true.

(i) In a right triangle the hypotenuse is the .... side.

(ii) The sum of three altitudes of a triangle is ..... than its perimeter.

(iii) The sum of any two sides of a triangle is .... than the third side.

(iv) If two angles of a triangle are unequal, then the smaller angle has the side opposite to it.

(v) Difference of any two sides of a triangle is than the third side.

(vi) If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.

Answer 1

(i) In a right triangle the hypotenuse is the largest side

Reason: Since a triangle can have only one right angle, other two angles must be less than 90°

⇒The right angle is the largest angle

⇒Hypotenuse is the largest side.

(ii) The sum of three altitudes of a triangle is less than its perimeter

(iii) The sum of any two sides of a triangle is greater than the third side.

(iv) If two angles of a triangle are unequal, then the smaller angle has the smaller side opposite to it.

(v) Difference of any two sides of a triangle is less than the third side.

(vi) If two sides of a triangle are unequal, then the larger side has greater angle opposite to it.