Math, asked by Krishna706578, 7 months ago

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Answered by mahendra78965479
1

Answer:

to prove: AE =to BE, TRIANGLE DAE IS EQUAL TO 15

proof: triangle EDC is equilateral triangle so

Step-by-step explanation:

de=ce tir ECDis equilateral triangle

DA=CB because ABCD is a square

so,

DA=CB

ED=EC

SO, AB=DC because equilateral triangle and square equilateral triangle all sides are equal and in a square all sides are equal so AB equel to DC

So,

AE=BE

Tri AED congruent to Tri BECBEC

because all sides are equal

to prove: angle DAE is 15 degree

proof: angle aed is 15 degree becauseequilateral triangle all sides are equal and in this triangle angle DEC is divied in to 3 parts angle DEC =15, angle aeb=15 and angle ebc is=30

in triangle aed angle aed =15

DA=DE SIDES ARE EQUAL

SO,angle DAE =15 degree because sides are equal so opposite angles are also equal

so,

angle DAE is equal to 15 degree

hence proved

MARK AS A BRAINLIST

Answered by anindyaadhikari13
2

\star\:\:\:\bf\large\underline\blue{Question:-}

In the adjoining figure, ABCD is a square and \Delta EDC is an equilateral triangle. Prove that,

  1. AE = BE.
  2. \angle DAE=15\degree

\star\:\:\:\bf\large\underline\blue{Proof:-}

Since, ABCD is a square, therefore,

AB=BC=CD=AD.

Now, \Delta DCE is an equilateral triangle.

So,

DC=CE=DE.

Also,

\angle ADC=\angle BCD=90\degree\:\:.......(i).

And,

\angle EDC=\angle DCE =60\degree\:\:.......(ii) /*Since \Delta EDC is an equilateral triangle */

Combining equation (i) and (ii), we get,

\angle ADE = \angle BCE

In \Delta AED and \Delta BCE.

  1. AD=BC (ABCD is a square)
  2. DE = EC (Sides of equilateral triangle).
  3. \angle ADE = \angle BCE (Proved earlier) .

Therefore,

\Delta ADE \cong \Delta BCE (By SAS)

So,

  • AE=BE (c.p.c.t) (Proved part (i))

Now,

ABCD is a square and sides of triangle DCE are equal to the sides of the square.

So,

AD=DE.

Therefore,

Triangle ADE is an equilateral triangle.

So,

\angle DAE=\angle DEA.

Now,

\angle ADE=\angle ADC+\angle EDC

\implies \angle ADE = 150\degree.

So,

\angle DAE=\angle DEA=\frac{180\degree-150\degree}{2}=15\degree.

Hence Proved.

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