ABCD is a square X is the mid point of AB and Y is the mid point of BC Consider the following statem...........

Quantitative Aptitude (CDS) Coordinate Geometry

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ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements :

1. Triangles ADX and BAY are congruent.

2. $\small \angle$ DXA = $\small \angle$ AYB.

3. DX is inclined at an angle 60o with AY.

4. DX is not perpendicular to AY.

Which of the above statements are correct?

2, 3 and 4 only

1, 2 and 4 only

1, 3 and 4 only

1 and 2 only

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Explanation:

Statement 1:
In triangle ADC and triangle BAY
∠A = ∠B = 90⁰
AX = BY [Half of the side of squre]
AD = AB
By SAS,
Triangle ABY ≅ triangle DAX
Hence statement 1 is correct.
Statement 2:
By CPCT,
Clearly, ∠DXA = ∠AYB
Hence statement 2 is correct.
Statement 3:
We can say anything about
inclination of DX with AY.
Hence statement 3 is incorrect.
Statement 4:
Clearly, DX is not perpendicular to
AY.
Hence statement 4 is incorrect.
Hence only statement 1 and 2 are
correct.
Hence option (4)