Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.
Solution No, it is not possible to construct a triangle with lengths of sides 4 cm, 3 cm and 7... View Article
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“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
Solution No, the given statement is True Reason Because by the congruent rule, the triangles will be congruent either by ASA rule... View Article
“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
Solution No, the given statement is false, Reason Because by the congruent rule, The two sides and the included angle... View Article
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side BC of Δ ABC so that the two triangles are congruent? Give reason for your answer.
Given In ΔABC and ΔPQR, ∠A = ∠Q and ∠B = ∠R and ΔABC and ΔPQR are congruent triangles Find... View Article
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side AB of Δ ABC so that the two triangles are congruent? Give reason for your answer.
Given In ΔABC and ΔPQR, ∠A = ∠Q and ∠B = ∠R and ΔABC and ΔPQR are congruent triangles Find... View Article
In Δ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is (A) 4 cm (B) 5 cm (C) 2 cm (D) 2.5 cm
The correct answer is (A) 4 cm Solution According to the given details In ΔPQR ∠R = ∠P QR = 4 cm ... View Article
In Δ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to (A) 80° (B) 40° (C) 50° (D) 100°
The correct answer is (C) 50° Solution According to the given details In Δ ABC BC = AB ∠B = 80°... View Article
In Δ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to (A) 40° (B) 50° (C) 80° (D) 130°
The correct answer is (B) 50° Solution According to the given details In Δ ABC AB = AC ∠B = 50°.... View Article
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... 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... 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... 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:... 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... 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... 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... 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... 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... 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... 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... View Article
