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Can a triangle have two obtuse angles? Give reason for your answer.

No. A triangle cannot have two obtuse angles Solution According to the angle sum property, the sum of interior angles of a triangle is... View Article

Can a triangle have all angles less than 60°? Give reason for your answer.

No. A triangle cannot have all angles less than 60° Solution According to the angle sum property, the sum of interior angles of a... View Article

For what value of x + y in Figure will ABC be a line? Justify your answer.

Solution: The value of x + y should be 180o for ABC to be a line. Justification: From the given diagram we note that BD is a ray... View Article

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

The correct answer is (A) An acute-angled triangle Solution According to the given details The angles of a triangle are of the ratio 5 :... View Article

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is (A) 37 1/2o (B) 52 1/2o (C) 72 1/2o (D) 75°

The correct answer is (B) 52 ½o Solution According to the given details The exterior angle of the triangle= 105° Let the two... View Article

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

The correct answer is (D) A right triangle Solution Let the angles of △PQR be ∠P, ∠Q and ∠R Given that ∠P=... View Article

In Figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to (A) 85° (B) 135° (C) 145° (D) 110°

The correct answer is (C) 145° Solution According to the diagram given AB || CD || EF PQ || RS ∠RQD = 25° ∠CQP =... View Article

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.]

Solution For every line L and for every point P not lying on L, there exists a unique line M passing through P and parallel to L. Two distinct... View Article

Read the following statement: 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 an equilateral triangle.

Solution Defined terms are listed below: (1) Equilateral triangle: An equilateral triangle is a triangle with all three sides of equal length... View Article

In the figure we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that BX = BY. Solve the following question using appropriate Euclid’s axiom.

Solution: Given BX = ½ AB BY = ½ BC AB = BC To Prove BX = BY ⇒ 2BX = AB ….(i) ⇒ 2BY =... View Article

In the figure we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC. Solve the following question using appropriate Euclid’s axiom.

Solution: Given X is the mid-point of AC Y is the mid-point of BC. To Prove AC=BC Proof AX = CX= ½ AC ⇒ 2AX =2CX... View Article

In the figure we have AB = BC, BX = BY. Show that AX = CY. Solve the following question using appropriate Euclid’s axiom.

Solution: According to the given details we observe that AB =BC …(i) and BX=BY …(ii) According to Euclid’s axiom,... View Article

Look at the figure Show that length AH > sum of lengths of AB + BC + CD. Solve the following question using appropriate Euclid’s axiom.

Solution: According to the given figure, we observe that AB+BC+CD =AD Here, AD is a part of AH. According to Euclid’s axiom,... View Article

It is known that x + y = 10 and that x = z. Show that z + y = 10? Solve the following question using appropriate Euclid’s axiom.

Solution According to the given details we get to know that x+y=10 …(i) And, x=z …(ii) On applying Euclid’s axiom,... View Article

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. Solve the following question using appropriate Euclid’s axiom.

Solution Let the sale of both the salesmen in August = S. According to the given details, we get to know that In September, each salesman... View Article

Write whether the following statements are True or False? Justify your answer: 1. Euclidean geometry is valid only for curved surfaces. 2. The boundaries of the solids are curves. 3. The edges of a surface are curves. 4. The things which are double of the same thing are equal to one another.

1. Euclidean geometry is valid only for curved surfaces. Answer The given statement is False Solution Euclidean geometry is valid only for... View Article

The side faces of a pyramid are: (A) Triangles (B) Squares (C) Polygons (D) Trapeziums

The correct answer is (A) Triangles Solution The side faces of a pyramid are triangles.... View Article

A pyramid is a solid figure, the base of which is (A) Only a triangle (B) Only a square (C) Only a rectangle (D) Any polygon

The correct answer is (D) Any polygon Solution A pyramid is a solid figure, the base of which can be a triangle, a square or some other... View Article

In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio (A) 1 : 3 : 4 (B) 4 : 2 : 1 (C) 4 : 4 : 1 (D) 4 : 3 : 2

The correct answer is (B) 4 : 2 : 1 Solution In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having... View Article

Boundaries of surfaces are: (A) Surfaces (B) Curves (C) Lines (D) Points

The correct answer is (B) Curves Solution The boundaries of surfaces are curves. A surface is something that has length and breadth only.... View Article

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