English

Which of the Following Statements Are True (T) and Which Are False (F)? Difference of Any Two Sides of a Triangle is Equal to the Third Side.

Advertisements
Advertisements

Question

Which of the following statements are true (T) and which are false (F)? 

Difference of any two sides of a triangle is equal to the third side. 

Advertisements

Solution

False (F)
Reason: The difference of any two sides of a triangle is less than third side.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Congruent Triangles - Exercise 12.6 [Page 81]

APPEARS IN

R.D. Sharma Mathematics [English] Class 9
Chapter 12 Congruent Triangles
Exercise 12.6 | Q 8.4 | Page 81

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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:

  1. OB = OC
  2. AO bisects ∠A

In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.


If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 


Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O. 


PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.  

 


ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles  


Fill the blank in the following so that the following statement is true. 

Angle opposite to equal sides of a triangle are ..... 


Fill the blank in the following so that the following statement is true. 

In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.


In a ΔABC, if ∠B = ∠C = 45°, which is the longest side? 


Which of the following statements are true (T) and which are false (F)? 

Sum of any two sides of a triangle is greater than the third side. 

 


Fill in the blank to make the following statement true. 

In a right triangle the hypotenuse is the .... side. 


Fill in the blank to make the following statement true. 

If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it. 


If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.


In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =


Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =


In the given figure, what is z in terms of x and y?


In the given figure, what is the value of x?


In the given figure, if l1 || l2, the value of x is


In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.


ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:


In ∆ABD and ∆ACD,

AB = AC (Given)

∠B = ∠C (Because AB = AC)

and ∠ADB = ∠ADC

Therefore, ∆ABD ≅ ∆ACD (AAS)

So, ∠BAD = ∠CAD (CPCT)

What is the defect in the above arguments?

[Hint: Recall how ∠B = ∠C is proved when AB = AC].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×