English

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. - Mathematics

Advertisements
Advertisements

Question

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. 

Advertisements

Solution

False (F)
Reason: Since two sides are equal, the triangle is an isosceles triangle. 
⇒ The two altitudes corresponding to two equal sides must be equal.  

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Congruent Triangles - Exercise 12.5 [Page 62]

APPEARS IN

RD Sharma Mathematics [English] Class 9
Chapter 12 Congruent Triangles
Exercise 12.5 | Q 5.7 | Page 62

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 


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. 

 


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. 


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

The measure of each angle of an equilateral triangle is 60° 

 


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

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


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


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)?  

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. 


Fill in the blank to make the following statement true.  

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


If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?


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


In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then


In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.


In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.


It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?


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


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].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×