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Lines & Angles

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°

Introduction To Euclid’s Geometry

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.

Introduction To Euclid’s Geometry

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.

Introduction To Euclid’s Geometry

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

Introduction To Euclid’s Geometry

Study the following statement:
“Two intersecting lines cannot be perpendicular to the same line”.
Check whether it is an equivalent version to the Euclid’s fifth postulate.
[Hint : Identify the two intersecting lines l and m and the line n in the above
statement.]

Introduction To Euclid’s Geometry

An equilateral triangle is a polygon made up of three line segments out of which
two line segments are equal to the third one and all its angles are 60° each.

Define the terms used in this definition which you feel necessary. Are there any
undefined terms in this? Can you justify that all sides and all angles are equal in a
equilateral triangle

Introduction To Euclid’s Geometry

Read the following statement:
“A square is a polygon made up of four line segments, out of which, length of three line
segments are equal to the length of fourth one and all its angles are right angles”.
Define the terms used in this definition which you feel necessary. Are there any undefined
terms in this? Can you justify that all angles and sides of a square are equal?

Introduction To Euclid’s Geometry

It is known that x + y = 10 and that x = z. Show that z + y = 10?

Introduction To Euclid’s Geometry

Two salesmen make equal sales during the month of August. In September, each
salesman doubles his sale of the month of August. Compare their sales in September

Introduction To Euclid’s Geometry

Solve the equation a – 15 = 25 and state which axiom do you use here.