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It is given that Δ ABC ≅ Δ RPQ. Is it true to say that BC = QR? Why?

Solution The given statement is False Reason As per the given condition Δ ABC ≅ Δ RPQ Hence, BC = PQ not BC = QR ... View Article

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 cm. Reason From the triangle inequality theorem we... View Article

“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 or... 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 of one triangle are equal... 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 out We have to... 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 out We have to... 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° Since, BC = AB... 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°. Since, AB = AC... 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 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

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