हिंदी

In a δAbc, If ∠B = ∠C = 45°, Which is the Longest Side? - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

Given that in ΔABC, 

∠B=∠C=45°  

We have to find longest side
We know that, 

Sum of angles in a triangle=180° 

⇒∠A+∠B+∠C=180° 

⇒∠A+45°+45°=180° 

⇒∠A=180°-(45°+45°)=180°-90°=90° 

∴ ∠A=90° 

  

 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Congruent Triangles - Exercise 12.6 [पृष्ठ ८१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 9
अध्याय 12 Congruent Triangles
Exercise 12.6 | Q 2 | पृष्ठ ८१

वीडियो 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

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.


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


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°. 


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 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): 

Sides opposite to equal angles of a triangle may be unequal 


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. 


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 = ...... 


Fill in the blank to make the following statement true. 

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


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


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, for which value of x is l1 || l2?


In the given figure, the value of x is ______.


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


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


Find all the angles of an equilateral triangle.


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].


In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×