Question

ABCD is a rectangle and klmn are the midpoints of the sides ab BC CD respectively if kn and is equal to 3 cm ab is equal to 5 cm and then find BD and LM what kind of quadrilateral is KLMN​

Answer 1

Step-by-step explanation:

ABCD is a square, so

AB = BC = CD = DA ...(1)

Also

AK = BL = CM = DN .....(2)

Subtracting (2) from (1)

We get

AB- AK = BC - BL = CD - CM = DA - DN

BK = CL = DM = AN ...(3)

So now we have

AK = BL = CM = DN

AN = BK= CL = DM

Squaring and adding

AK² + AN² = BL² + BK²= CM² + CL² = DN² + DM² ...(4)

But

By Pythagorean theorem (4) Becomes

KN² = KL² = LM² = NM²

So

KN = KL = LM = NM

So KLMN is a rhombus

But <1 = <3 as triangles are congruent

And < 1 + <2 = 90

So <2 + <3 = 90

Hence

Therefore KLMN is a square.

Answer 2

K,L,M and N are points on the sides AB,BC,CD and DA respectively of a square ABCD such that AK=BL=CM=DN. Prove that KLMN is a square

Share

Study later

ANSWER

As ABCD is a square, so

AB = BC = CD = DA ...(1)

Also

AK = BL = CM = DN .....(2)

Subtracting (2) from (1)

We get

AB- AK = BC - BL = CD - CM = DA - DN

BK = CL = DM = AN ...(3)

So now we have

AK = BL = CM = DN

AN = BK= CL = DM

Squaring and adding

AK² + AN² = BL² + BK²= CM² + CL² = DN² + DM² ...(4)

But

By Pythagorean theorem (4) Becomes

KN² = KL² = LM² = NM²

So

KN = KL = LM = NM

So KLMN is a rhombus

But <1 = <3 as triangles are congruent

And < 1 + <2 = 90

So <2 + <3 = 90

Hence

Therefore KLMN is a square.

please mark my ans as brain list♥️