Sides ab and ac of triangle abc are extended

Asked by admin @ in Math viewed by 341 People

"Question 2 In the given figure sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.

Class 9 - Math - Triangles Page 132"

Answered by admin @


Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.



Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.


Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.


The two axioms given above together are called the linear pair axioms.


____________________________________

Use the Inequality that the side opposite to the larger angle is longer, to show the inequality.


____________________________________


Given: ∆ABC is a Triangle &

∠PBC < ∠QCB


To Prove:

AC>AB



Proof:


∠ABC + ∠PBC = 180°
( by linear pair axiom)
⇒ ∠ABC = 180° – ∠PBC


also,

∠ACB + ∠QCB = 180°
(by Linear Pair axiom)
⇒ ∠ACB = 180° – ∠QCB


Since,

∠PBC < ∠QCB therefore, ∠ABC > ∠ACB


Here, the side opposite to the larger angle is longer.


Hence, AC > AB


========================================

Hope this will help you.....

Similar Questions

In an isosceles triangle abc with ab ac

Asked by admin @ in Math viewed by 377 persons

"Question 1 In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that: (i) OB …

Abc is an isosceles triangle with ab ac

Asked by admin @ in Math viewed by 275 persons

ABC is an isosceles triangle in which AB=AC.Side BA is produced to D Such that AD=AB.Show that BCD is a right angled triangle

Triangle abc is an isosceles triangle with ab ac

Asked by admin @ in Math viewed by 271 persons

ABC is an isosceles triangle in which AB=AC.Side BA is produced to D Such that AD=AB.Show that BCD is a right angled triangle

If abc is an isosceles triangle with ab ac

Asked by admin @ in Math viewed by 527 persons

if triangle ABC is an isosceles triangle such that AB=AC then prove that altitude AD from a on BC bisects it

Abc is an equilateral triangle of side 2a

Asked by admin @ in Math viewed by 368 persons

ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Draw a triangle abc with side bc 7cm

Asked by admin @ in Math viewed by 353 persons

Draw a triangle ABC with side BC=7cm, angle B=45,angle A=105. Then construct a triangle whose sides are 4/3 times the corresponding sides of triangle abc

Abc is an isosceles triangle with ac bc

Asked by admin @ in Math viewed by 356 persons

ABC is an isosceles triangle with AC = BC . If AB2 = 2AC2 . Prove that abc is a right angle triangle

In triangle abc prove that ab bc ca 2ab

Asked by admin @ in Math viewed by 347 persons

In triangle ABC prove that AB+BC+CA&gt;2AB

Side bc of triangle abc is produced to d

Asked by admin @ in Math viewed by 282 persons

the side of BC of triangle ABC is produced to D If the bisector of angle A meets BC in L. prove that angle abc + angle acd = 2 …

Draw a triangle abc with side bc 6 cm

Asked by admin @ in Math viewed by 325 persons

Draw a triangle ABC with side BC= 6cm ,AB=5cm and &lt;ABC=60° then construct a triangle whoss sides are 3/4 of the corresponding sides of the triangle ABC.

Line segment df intersect the side ac of a triangle

Asked by admin @ in Math viewed by 285 persons

In the given figure, line segment DF intersect the side AC of a triangle ΔABC at the point E such that E is the mid–point of CA and ∠AEF = …

What is the longest side of a right triangle called

Asked by admin @ in Mathematics viewed by 355 persons

What is the longest side of a right triangle called?

A triangle with 3 different sides in length is called

Asked by admin @ in Health viewed by 363 persons

A triangle with three different side lengths is called A. scalene. B. equilateral. C. isosceles. D. equiangular.

Find the length of side x in the right triangle

Asked by admin @ in Mathematics viewed by 372 persons

Which expression finds the length of side x in this right triangle?

How to find sides of a 30 60 90 triangle

Asked by admin @ in Mathematics viewed by 303 persons

In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

Most viewed questions in Math

What is the value of x in the expression

Asked by admin @ in Math viewed by 15151 persons

Shubham is facing south and moves 30 km

Asked by admin @ in Math viewed by 12987 persons

Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ in Math viewed by 12034 persons

Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ in Math viewed by 11518 persons

Survey of various types of bank accounts icse project

Asked by admin @ in Math viewed by 11506 persons

The town of p is located at point x

Asked by admin @ in Math viewed by 11359 persons

A clock gains 4 minutes after every 4 minutes

Asked by admin @ in Math viewed by 10167 persons

Running a tuck shop or canteen maths project pdf

Asked by admin @ in Math viewed by 9379 persons

Paul is sixteenth from the front of the row

Asked by admin @ in Math viewed by 9352 persons

The average weight of 20 teachers is 80 kg

Asked by admin @ in Math viewed by 7524 persons

The number 567 xy is completely divisible by 30

Asked by admin @ in Math viewed by 7396 persons

In a row of friends tiya occupies fifteenth place

Asked by admin @ in Math viewed by 7207 persons

What would $ mean if fat is coded as

Asked by admin @ in Math viewed by 5275 persons

Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4804 persons

Rahul went to his mother's mother in law

Asked by admin @ in Math viewed by 4179 persons