Question

c) ABCD is a square; X is a mid-point of AB and Y the mid-point of BC. Prove that
(i) the triangles ADX and BAY are congruent (ii) DXA = AYB ; (iii) DX is perpendicular to AY.

Answer 1

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Maths

Congruence of Triangles

Criteria for Triangle Congruence

ABCD is a square; X is the ...

MATHS

ABCD is a square; X is the mid-point of AB and Y the mid-point of BC.Hence, DX is perpendicular to AY.

If the above statement is true then mention answer as 1, else mention 0 if false.

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ANSWER

AB=BC (ABCD is a square)

∴

2

1

AB=

2

1

BC

∴AX=BY ...(X and Y are mid points of AB and BC respectively)

In △AXD and △ABY,

∠DAX=∠ABY (Each 90

∘

)

AX=BY (Proved above)

AD=AB (ABCD is a square)

Thus, △AXD≅△BYA ....(SAS test)

∠AXD=∠BYA (By cpct)

i.e ∠AXO=∠OYB ...(I)

Now, In quadrilateral XOYB,

Sum of angles = 360

∠XOY+∠OYB+∠YBX+∠BXO=360

o

∠XOY+∠OYB+90+180−∠AXO=360

o

But ∠OYB=∠AXO (From I)

hence, ∠XOY=90

∘

DX⊥AY

solution

Answer 2

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