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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
Which congruence criterion do you use in the following?
Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
| Steps | Reasons | ||
| 1 | PM = QM | 1 | ... |
| 2 | ∠PMA = ∠QMA | 2 | ... |
| 3 | AM = AM | 3 | ... |
| 4 | ΔAMP ≅ ΔAMQ | 4 | ... |
Explain, why ΔABC ≅ ΔFED.
ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.
Use the information in the given figure to prove:
- AB = FE
- BD = CF
If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.
In ∆ABC, AB = AC. Show that the altitude AD is median also.
A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.
In the following figure, OA = OC and AB = BC.
Prove that: ΔAOD≅ ΔCOD
In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.
Prove that QR bisects PC.
Hint: ( Show that ∆ QBP is equilateral
⇒ BP = PQ, but BP = CR
⇒ PQ = CR ⇒ ∆ QPM ≅ ∆ RCM ).
