A transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Give reason for your answer.
Let OA, OB, OC and OD are rays in the anticlockwise direction such that ∠ AOB = ∠COD = 100°, ∠BOC = 82° and ∠AOD = 78°. Is it true to say that AOC and BOD are lines?
Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is
(A) 60° (B) 40° (C) 80° (D) 20°
If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be
(A) 50° (B) 65° (C) 145° (D) 155°
The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is
(A) an acute angled triangle (B) an obtuse angled triangle
(C) a right triangle (D) an isosceles triangle
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(A) an isosceles triangle
(B) an obtuse triangle
(C) an equilateral triangle
(D) a right triangle
If two interior angles on the same side of a transversal intersecting
two parallel lines are in the ratio 2 : 3, then the greater of the two angles is
(A) 54° (B) 108° (C) 120° (D) 136°
Read the following axioms:
(i) Things which are equal to the same thing are equal to one another.
(ii) If equals are added to equals, the wholes are equal.
(iii) Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.
Read the following two statements which are taken as axioms :
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.
Is this system of axioms consistent? Justify your answer.
Read the following statements which are taken as axioms :
(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer
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