No products in the cart.

Chapter 7 theorem 7.6

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Chapter 7 theorem 7.6
  • 1 answers

Gaurav Seth 3 years, 10 months ago

“If two sides of a triangle are unequal then the longer side has greater angle opposite to it.”

Given: A ΔABC in which AC > AB (say)

To prove: ∠ABC > ∠ACB

Construction: Mark a point D on AC such that AB = AD.

Join BD.

Proof: In ΔABD

AB = AD (by construction)

⇒ ∠1 = ∠2 …(i) (angles opposite to equal sides are equal)

Now in ΔBCD

∠2 > ∠DCB (ext. angle is greater than one of the opposite interior angles)

⇒ ∠2 > ∠ACB …(ii) [∵ ∠ACB = ∠DCB]

From (i) and (ii), we get

∠1 > ∠ACB …(iii)

But ∠1 is a part of ∠ABC

∠ABC > ∠1 …..(iv)

Now from (iii) and (iv), we get

∠ABC > ∠ACB

Hence proved.

http://mycbseguide.com/examin8/

Related Questions

What is 38747484±393884747
  • 0 answers
Ch-1 introduction
  • 0 answers
3√2×4√2×12√32
  • 0 answers
2x+5y
  • 0 answers
X³-12x²+39x-28
  • 0 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Download myCBSEguide App