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ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD.

Given A right angles triangle with AB = AC bisector of ∠A meets BC at D. To Prove BC = 2 AD Proof According to given details From right... View Article

ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

Given ABCD is a quadrilateral AB = BC AD = CD To Prove BD bisects both the angles ABC and ADC Proof According to the given details... View Article

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

Given BP is the bisector of ∠ABC the line through P, parallel to BA meet BC at Q To Prove BPQ is an isosceles triangle. Proof... View Article

ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure. To prove that ∠BAD = ∠CAD, a student proceeded as follows: In Δ ABD and Δ ACD, AB = AC (Given) ∠B = ∠C (because AB = AC) And ∠ADB = ∠ADC Therefore, Δ ABD Δ Δ ACD (AAS) So, ∠BAD = ∠CAD (CPCT) What is the defect in the above arguments? [Hint: Recall how ∠B = ∠C is proved when AB = AC].

Solution: FromΔ ABD and Δ ADC, we note that ∠ADB = ∠ADC According to the given details AB = BC AD = AD [Common... View Article

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Fig. 7.12. Prove that the image is as far behind the mirror as the object is in front of the mirror. [Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection].

Solution: Let AB intersect LM at O. We have to prove that AO = BO. Now, Accoring to law of reflection ∠i = ∠r ---------(i) [∵Angle... View Article

Find all the angles of an equilateral triangle.

In equilateral triangle,all the sides are equal Therefore, all angles are also equal Let the angles of an equilateral triangle = A According... View Article

Q is a point on the side SR of a Δ PSR such that PQ = PR. Prove that PS > PQ.

Given In ΔPSR, Q is a point on the side SR such that PQ = PR. To Prove PS > PQ Proof From ΔPRQ, PR = PQ (given)... View Article

In Figure BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that Δ ABC ≅ Δ DEF.

Solution: According to the given details BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC.... View Article

CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that Δ ADE ≅ Δ BCE.

According to the given details CDE is an equilateral triangle formed on a side CD of a square ABCD. From ΔADE and ΔBCE, DE = CE... View Article

In Figure D and E are points on side BC of a Δ ABC such that BD = CE and AD = AE. Show that Δ ABD ≅ Δ ACE.

Solution: According to the details given From ΔABC, BD = CE and AD = AE. From ΔADE, AD = AE Since opposite angles to equal... View Article

ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.

Given BC is an isosceles triangle with AB = AC BD and CE are its two medians To Prove BD = CE. Proof From ΔABD and ΔACE,... View Article

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.