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प्रश्न
In two triangles ABC and ADC, if AB = AD and BC = CD. Are they congruent?
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उत्तर
The given information and corresponding figure is given below
AB = AD
BC = CD

From the figure, we have
AB = AD (given)
CB = CD (given)
And,
AC = AC (common sides)
Hence, triangles ABC and ADC are congruent to each other.
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संबंधित प्रश्न
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
- ΔABD ≅ ΔBAC
- BD = AC
- ∠ABD = ∠BAC.

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AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that
- ΔDAP ≅ ΔEBP
- AD = BE

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
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- ∠DBC is a right angle.
- ΔDBC ≅ ΔACB
- CM = `1/2` AB

Which congruence criterion do you use in the following?
Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB

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- AB = FE
- BD = CF

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Prove that:
(i) ΔDCE ≅ ΔLBE
(ii) AB = BL.
(iii) AL = 2DC
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
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In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.
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