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Areas of Parallelograms and Triangles
Question
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In figure, ∠B = ∠.E, BD = CE and ∠1 = ∠2. Show ∆ABC ≅ ∆AED.

Answer

Given: In figure,
∠B = ∠E, BD = CE
and    ∠1 = ∠2
To Prove: ∆ABC ≅ ∆AED
Proof: ∠1 = ∠2
⇒ ∠1 + ∠DAC = ∠2 + ∠DAC
⇒ ∠BAC = ∠EAD    ...(1)
BD = CE
⇒ BD + DC = CE + DC
⇒    BC = ED    ...(2)
∠B = ∠E    ...(3)
In view of (1), (2) and (3),
∆ABC ≅ ∆AED
| AAS congruence rule

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Some More Questions From Areas of Parallelograms and Triangles Chapter

In figure, PS = QR and ∠SPQ = ∠RQP. Prove that PR = QS and ∠QPR = ∠PQS.

In figure, AP and BQ are perpendiculars to the line-segment AB and AP = BQ. Prove that O is the midpoint of line segments AB and PQ.

In figure, diagonal AC of a quadrilateral ABCD bisects the angles A and C. Prove that AB = AD and CB = CD.

AB is a line-segment. AX and BY are two equal line-segments drawn on opposite sides of line AB such that AX || BY. If AB and XY intersect each other at P. Prove that:
(i)    ∆APX ≅ ∆BPY
(ii)    AB and XY bisect each other at P.

In figure, ∠QPR = ∠PQR and M and N are respectively points on sides QR and PR of ∆PQR, such that QM = PN. Prove that OP = OQ, where O is the point of intersecting of PM and QN.

In figure, ∠B = ∠.E, BD = CE and ∠1 = ∠2. Show ∆ABC ≅ ∆AED.

In figure given below, AD is the median of ∆ABC.
BE ⊥ AD, CF ⊥ AD. Prove that BE = CF.

In the given figure, if AB = FE, BC = ED, AB ⊥ BD and FE ⊥ EC, then prove that AD = FC.

In figure, OA = OB and OD = OC. Show that:
(i) ∆AOD ≅ ∆BOC and (ii) AD = BC.