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 ${60}^{\circ }$

(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 the triangle need not be equal

(viii) If any two sides of a right triangle are respectively equal to two sides of another 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 ar equal.

(ii) True.

(iii) True.

(iv) True

(v) True.

(vi) True.

(vii) False: The attitude an equal.

(viii) False : If one side and hypotenuse of right triangle on one side and hypotenuse of the other right triangle are equal, the triangles are congruent.

(ix) True.