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.
Answers
(i) Sides opposite to equal angles of a triangle may be unequal.
FALSE
(ii) Angles opposite to equal sides of a triangle are equal.
TRUE
(iii) The measure of each angle of an equilateral triangle is 60°.
TRUE
(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
FALSE
(v) The bisectors of two equal angles of a triangle are equal.
TRUE
(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
FALSE
(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.
FALSE
(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.
FALSE
(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.
TRUE
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