In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE - Future Study Point

# In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE

## In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that ∠ B = ∠E

NCERT Solutions Class 10 Science from chapter 1 to 16

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Question.In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE

We are given two right triangles ΔABC and ΔDEF in which sinB =sinE

Let ∠A and ∠D are  right triangles of ΔABC and ΔDEF respectively

GIVEN : sinB = sinE

TO PROVE: ∠B =∠E

Proof: In ΔABC and ΔDEF

sinB = sinE

BC = kEF  & AC = kDF……(i)

Applying Pythagoras theorem in both triangles ΔABC and ΔDEF, we have

Putting the value of BC and AC in the equation  (i)

Since we have to prove the angles of two triangles, so we are needed to prove both triangles similar to each other.

And proving both triangles similar to each other, here we have to prove all three sides in proportional to each other.

From (i),(ii) and (iii) we have

∴ΔABC ∼ DEF (SSS rule)

Hence ∠B =∠E

OR

you can understand it through our video

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### NCERT Solutions for class 10 maths

 Chapter 1-Real number Chapter 9-Some application of Trigonometry Chapter 2-Polynomial Chapter 10-Circles Chapter 3-Linear equations Chapter 11- Construction Chapter 4- Quadratic equations Chapter 12-Area related to circle Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume Chapter 6-Triangle Chapter 14-Statistics Chapter 7- Co-ordinate geometry Chapter 15-Probability Chapter 8-Trigonometry

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