मराठी

Which of the Following Statements Are True (T) and Which Are False (F)? Sum of the Three Sides of a Triangle is Less than the Sum of Its Three Altitudes. - Mathematics

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प्रश्न

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

Sum of the three sides of a triangle is less than the sum of its three altitudes. 

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उत्तर

False (F)
Reason: Sum of these sides of a triangle is greater than sum of its three altitudes 

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Congruent Triangles - Exercise 12.6 [पृष्ठ ८१]

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आरडी शर्मा Mathematics [English] Class 9
पाठ 12 Congruent Triangles
Exercise 12.6 | Q 8.1 | 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

AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB. 

 


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

  


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.


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. 


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): 

Angles opposite to equal sides of a triangle are equal 


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

The bisectors of two equal angles of a triangle are equal 


In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle. 

 


O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC 
(iii) OA + OB + OC >` 1/2`(AB + BC + CA) 


In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC  

 


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

Sum of any two sides of a triangle is greater than twice the median drawn to the third side. 


In the given figure, x + y =


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


In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.


In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason for your answer.


AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.


Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.


CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.


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