हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 4 cm

  • 5 cm

  • 2 cm

  • 2.5 cm

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

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

Explanation:

Given, ∆PQR such that ∠R = ∠P, QR = 4 cm and PR = 5 cm

In ∆PQR, ∠R = ∠P

⇒ PQ = QR  ...[Sides opposite to equal angles are equal]

⇒ PQ = 4 cm  ...[∵ QR = 4 cm]

Hence, the length of PQ is 4 cm.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Triangles - Exercise 7.1 [पृष्ठ ६४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 9
अध्याय 7 Triangles
Exercise 7.1 | Q 5. | पृष्ठ ६४

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 figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD 

 


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


In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle. 


Prove that each angle of an equilateral triangle is 60°. 


Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral. 


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. 

 


Prove that the perimeter of a triangle is greater than the sum of its altitudes. 


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


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

Difference of any two sides of a triangle is equal to the third side. 


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


If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.


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 =


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


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


Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 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].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×