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Which of the Following Statements Are True (T) and Which Are False (F): the Bisectors of Two Equal Angles of a Triangle Are Equal - Mathematics

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प्रश्न

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

The bisectors of two equal angles of a triangle are equal 

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उत्तर

True (T)  

Reason: Since it an isosceles triangle, the lengths of bisectors of the two equal angles are equal

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पाठ 12: Congruent Triangles - Exercise 12.5 [पृष्ठ ६२]

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आरडी शर्मा Mathematics [English] Class 9
पाठ 12 Congruent Triangles
Exercise 12.5 | Q 5.5 | पृष्ठ ६२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

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respectively. Prove that LN = MN. 

 


ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles. 


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.


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

In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……


In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC 


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. 


Fill in the blank to make the following statement true. 

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

 


Fill in the blank to make the following statement true.  

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


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.


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


In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =


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Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC


Find all the angles of an equilateral triangle.


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)

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


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