Question

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Answer 1

(i) False:

Sides opposite to equal angles of a triangle are equal.

(ii) True:

Since, the sides are equal, the corresponding opposite angles must be equal.

(iii) True:

Since, all the three angles of an equilateral triangle are equal and sum of the three angles is 180 o , so each angle will be equal to \(\frac{180}{3}\)= 60°

(iv) False:

Here, the altitude from the vertex is also the perpendicular bisector of the opposite side. Here the triangle must be isosceles and may be an equilateral triangle.

(v) True:

Since, it is an isosceles triangle, the length of bisector of the two angles are equal.

(vi) False:

The angular bisector of the vertex angle is also a median. The triangle must be an isosceles and an equilateral triangle.

(vii) False:

Since, two sides are equal the triangle must be an isosceles triangle. The two altitudes corresponding to two equal sides must be equal.

(viii) False:

The two right triangles may or may not be congruent.

(ix) True:

According to RHS congruence the given statement is true.