हिंदी

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.

Advertisements
Advertisements

प्रश्न

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.  

Advertisements

उत्तर

False (F)
Reason: Here the altitude from thee vertex is also the perpendicular bisector of the opposite side.
⇒  The triangle must be isosceles and may be an equilateral triangle.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Congruent Triangles - Exercise 12.5 [पृष्ठ ६२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 9
अध्याय 12 Congruent Triangles
Exercise 12.5 | Q 5.4 | पृष्ठ ६२

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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 a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C. 

 


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


Prove that the medians of an equilateral triangle are equal. 


In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 


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. 


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


P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.  

 


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): 

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. 

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


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.


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 


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

 


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) 


Write the sum of the angles of an obtuse triangle.


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


In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =


In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is


In the given figure, x + y =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×