Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

The document Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Exercise 6.2
Q.1. In figures (i) and (ii), DE y BC. Find EC in (i) and AD in (ii).
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Sol. 
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
[By basic proportional theorem]
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
(ii) In ΔABC, DE || BC
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
[By basic proportional theorem]
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

Q.2. E and F are points on the sides PQ and PR respectively of a ΔPQR. 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
Sol. (i) Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
⇒ EF is not parallel to QR
[By converse of B.P.T.]
(ii) Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
⇒ EF || QR [By converse of B.P.T.]
(iii) Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
⇒ EF || QR [By converse of B.P.T.]

Q.3. In the figure, if LM || CB and LN || CD, prove that Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev.
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Sol. 

Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
From equation (i) and (ii)
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

Q.4. In the figure, DE || AC and DF || AE. Prove that
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Sol. In ΔABC,
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
From equation (i) and (ii)
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

Q.5. In the figure, DE || OQ and DF || OR. Show that EF || QR.
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Sol. In Δ PQO,
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
In ΔPOR, DF || OR
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev     ...(ii)
From equation (i) and (ii), we get
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
∴  EF || QR [By converse of B.P.T.]

Q.6. In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Sol. In Δ PQR,
AB || PQ
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
In ΔPOR, AC || PR
∴  OP/PA = OR/RC    .......(ii)

From equation (i) and (ii), we get
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
BC || QR [By converse of B.P.T.]

Q.7. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. 
Sol. Given: In Δ ABC, D is the mid-point of AB and DE || BC
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
To Prove: AE = EC
Proof: In ΔABC,
DE || BC
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
[By B.P.T.]
But AD = DB
⇒ AD/DB = 1
⇒ 1 = AE/EC ⇒ AE = EC
Hence, DE bisects AC.

Q.8. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
Sol. Given. A ΔABC in which D and E are mid-points of sides AB and AC respectively.
To Prove: DE || BC
Proof: In ΔABC, AD = DB and AE = EC
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
∴ DE || BC   [By converse of B.P.T.]

Q.9. ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev.
Sol.
Given: ABCD is a trapezium in which AB || DC
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Construction: Draw EO || DC
Proof: In ΔABD, EO || DC     [By construction]
DC || AB     [Given]
⇒  EO || AB
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

From equation (i) and (ii)

Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

Q.10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev. Show that ABCD is a trapezium.
Sol. Given: A quadrilateral ABCD, whose diagonals intersect at O.
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
To Prove: ABCD is a trapezium.
Construction: Draw EO || AB
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Proof: In ΔABC, OE || AB
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
From equation (i) and (ii)
Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev
⇒ OE || DC [By converse of B.P.T.]
OE || AB and OE || DC ⇒ AB || DC
∴ ABCD is a trapezium.

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

Viva Questions

,

Summary

,

study material

,

Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

,

Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

,

shortcuts and tricks

,

Exam

,

Free

,

past year papers

,

Sample Paper

,

Previous Year Questions with Solutions

,

mock tests for examination

,

ppt

,

Ex 6.2 NCERT Solutions- Triangles Class 10 Notes | EduRev

,

MCQs

,

Semester Notes

,

pdf

,

Objective type Questions

,

practice quizzes

,

video lectures

,

Important questions

,

Extra Questions

;