NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.2

 

 

NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.2

 

Question 1.
In the given figure (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
Solution:

 

Question 2.
E and F are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether EF || QR:
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Solution:

Question 3.
In the given figure, if LM || CB and LN || CD.
Prove that \(\frac { AM }{ AB } =\frac { AN }{ A{ D }^{ \bullet } } \)
Solution:

Question 4.
In the given figure, DE || AC and DF || AE.
Prove that \(\frac { BF }{ FE } =\frac { BE }{ E{ C }^{ \bullet } } \)
Solution:

Question 5.
In the given figure, DE || OQ and DF || OR. Show that EF || QR.
Solution:

Question 6.
In the given figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Solution:

Question 7.
Using B.P.T., prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that your have proved it in class IX)
Solution:

Question 8.
Using converse of B.P.T., prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that your have done it in class IX)
Solution:

Question 9.
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that \(\frac { AO }{ BO } =\frac { CO }{ D{ O }^{ \bullet } } \)
Solution:

Question 10.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that \(\frac { AO }{ BO } =\frac { CO }{ D{ O }^{ \bullet } } \) Show that ABCD is a trapezium.
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.2 in Hindi Medium

Q1. आकृति 6.17 (i) और (ii) में, DE || BC में AD ज्ञात कीजिए :

हल: (i)

Δ ABC में

DE || BC दिया है |

अत: आधारभूतिक समानुपातिक प्रमेय से

Q2. किसी त्रिभुज PQR की भुजाओं PQ और PR पर क्रमशः बिन्दु E और F स्थित हैं | निम्नलिखित में से प्रत्येक स्थिति के लिए, बताइए कि क्या EF|| QR है |

(i) PE = 3.9 cm, EQ= 3cm, PF = 3.6 और FR= 2.4 cm

(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm और RF = 9 cm

(iii) PQ = 1.28 cm, PR = 2.56 cm, 0.18 cm और PF = 0.36 cm

इसलिए, EF|| QR नहीं है |

Q7. प्रमेय 6.1 का प्रयोग करते हुए सिद्ध कीजिए कि एक त्रिभुज की एक भुजा के मध्य -बिन्दु से होकर दूसरी भुजा के समांतर खींची गई रेखा तीसरी भुजा को समद्धिभाजित करती है | (याद कीजिए की आप इसे कक्षा IX में सिद्ध कर चुके हैं|)

​Q8. प्रमेय 6.2 का प्रयोग करते हुए सिद्ध कीजिए की एक त्रिभुज की किन्ही दो भुजाओं के मध्य बिन्दुओं को मिलाने वाली रेखा तीसरी भुजा के समांतर होती है | (याद कीजिए की आप कक्षा IX में ऐसा कर चुके हैं ) |

Proved