Gujarat Board Solutions Class 10 Maths Chapter 6 Triangle Ex 6.2

Gujarat Board Solutions Class 10 Maths Chapter 6 Triangle Ex 6.2

Gujarat Board Textbook Solutions Class 10 Maths Chapter 6 Triangle Ex 6.2

Question 1.
In figure (i) and (ii). DE II BC. Find EC in (i) and AD in (ii).

Question 7.
Using theorem 6.1 (i.e. Basic proportionality theorem), prove that line drawn through the mid point of one side of a triangle parallel to another side bisects the third side (Recall that you have proved it in class IX) (CBSE 2012)
Solution:
Given:
∆ABC in which, D is the midpoint of AB and
DE || BC

Question 8.
Using theorem 6.2 (i.e. Converse of basic proportionality theorem), prove that the line joining the midpoints of any two sides a triangle is a parallel to the third side (Recall that you have done it in class IX)
Solution:
Given: ∆EC in which D and E are the midpoints of sides AB and AC respectively. DE is the line joining D and E.

∴ In ∆ADC
OE || CD (by converse of BPT)
But OE || AB (by construction)
therefore AB ||CD
Hence quadrilateral ABCD is a trapezium.

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