Archives

If AB = QR, BC = PR and CA = PQ, then (A) Δ ABC ≅ ΔPQR (B) ΔCBA ≅ ΔPRQ (C) ΔBAC ≅ Δ RPQ (D) Δ PQR ≅ Δ BCA

The correct answer is (B) ΔCBA ≅ ΔPRQ Solution According to the given details AB = QR, BC = PR and CA = PQ Since, AB = QR,... View Article

Which of the following is not a criterion for congruence of triangles? (A) SAS (B) ASA (C) SSA (D) SSS

The correct answer is (C) SSA Solution Two triangles are said to be congruent if all three corresponding sides are equal and all the three... View Article

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Solution: Let us assume that AB ║ CD EF be the transversal passing through the two parallel lines at P and Q respectively. PR and QS... View Article

Bisectors of interior ∠B and exterior ∠ACD of a Δ ABC intersect at the point T. Prove that ∠ BTC = 1/2 ∠ BAC.

Given: △ ABC, produce BC to D and the bisectors of ∠ABC and ∠ACD meet at point T. To prove: ∠BTC = ∠BAC Proof: In... View Article

If two lines intersect, prove that the vertically opposite angles are equal.

From the diagram, we observe that AB and CD intersect each other at point O. Let us assume the two pairs of vertically opposite angles to be,... View Article

In Figure BA || ED and BC || EF. Show that ∠ABC = ∠DEF [Hint: Produce DE to intersect BC at P (say)].

Construction: Extend DE to intersect BC at point, P. Given EF||BC and DP is the transversal, BA || ED and BC || EF. To Prove... View Article

If in Figure bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m.

Solution: l || m and t is the transversal ∠MAB = ∠SBA [alternate angles] ⇒ ½ ∠MAB = ½ ∠SBA ⇒ ∠PAB =... View Article

AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (Fig. 6.11). Show that AP || BQ.

Given OD is the bisector of ∠AOC OE is the bisector of ∠BOC OD ⊥ OE. To Prove A, O and B are collinear. Proof Since,... View Article

In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

Given ∠1 = 60° and ∠6 = 120° To Prove m and n are parallel Proof ∠1 = 60° and ∠6 = 120° Also,... View Article

How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.

Infinitely many triangles can be drawn having its angles as 53°, 64° and 63°. Solution According to the angle sum... View Article

How many triangles can be drawn having its angles as 45°, 64° and 72°? Give reason for your answer.

No. A triangle cannot be drawn having its angles as 45°, 64° and 72°. Solution According to the angle sum property, the sum of... View Article

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

M	T	W	T	F	S	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30