मराठी

Which of the Following Statements Are True (T) and Which Are False (F)? of All the Line Segments that Can Be Drawn from a Point to a Line Not Containing It, The Perpendicular Lin

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प्रश्न

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

Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one. 

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उत्तर

True (T) 

Reason: The perpendicular distance is the shortest distance from a point to a line not containing it.

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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 8.6 | 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

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


Determine the measure of each of the equal angles of a right-angled isosceles triangle.


BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE. 


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. 


ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°. 


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

The bisectors of two equal angles of a triangle are equal 


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

In an equilateral triangle all angles are ..... 


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

In a ΔABC if ∠A = ∠C , then AB = ...... 


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


Fill in the blank to make the following statement true. 

The sum of three altitudes of a triangle is ..... than its perimeter. 


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.


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


In the given figure, x + y =


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


The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =


If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is


Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.


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.


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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