English

Which of the Following Statements Are True (T) and Which Are False (F): If the Bisector of the Vertical Angle of a Triangle Bisects the Base, Then the Triangle May Be Isosceles. - Mathematics

Advertisements
Advertisements

Question

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

If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. 

Advertisements

Solution

False (F)
Reason: The angular bisector of the vertex angle is also a median
⇒  The triangle must be an isosceles and also may be an equilateral triangle.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Congruent Triangles - Exercise 12.5 [Page 62]

APPEARS IN

RD Sharma Mathematics [English] Class 9
Chapter 12 Congruent Triangles
Exercise 12.5 | Q 5.6 | Page 62

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Prove that the medians of an equilateral triangle are equal. 


In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN. 

 


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  


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

Sides opposite to equal angles of a triangle may be unequal 


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

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


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


Fill in the blank to make the following statement true. 

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

 


In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.


Write the sum of the angles of an obtuse triangle.


If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.


In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.


In the given figure, if AB ⊥ BC. then x =


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


In the given figure, the value of x is ______.


In the given figure, if BP || CQ and AC = BC, then the measure of x is


In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.


D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.


In ∆PQR, if ∠R > ∠Q, then ______.


Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.


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×