मराठी

Which of the Following Statements Are True (T) and Which Are False (F)? If Two Angles of a Triangle Are Unequal, Then the Greater Angle Has the Larger Side Opposite to It.

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प्रश्न

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

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

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उत्तर

True (T)
Reason: The side opposite to greater angle is longer and smaller angle is shorter in a triangle

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पाठ 12: Congruent Triangles - Exercise 12.6 [पृष्ठ ८१]

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आर.डी. शर्मा Mathematics [English] Class 9
पाठ 12 Congruent Triangles
Exercise 12.6 | Q 8.5 | पृष्ठ ८१

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

ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.


In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT 

  


If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.  


In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC. 


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. 

 


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

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.  


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. 


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

The two altitudes corresponding to two equal sides of a triangle need not be equal. 


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

Sides opposite to equal angles of a triangle are ...... 


Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm? 

 


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. 


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


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


The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.


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


In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.


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].


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