Question 1: Find the value of in each of the following figures:
Answer:
i)
Similarly,
ii)
We know
Question 2: State giving reasons, whether it is possible to construct a triangle or not with sides of lengths:
i) ii)
iii) iv)
Answer: (Note: The sum of any two sides of a triangle is always greater than the third side)
i) Not Possible to construct the triangle because (3+4 not greater than 7
ii) Possible to construct the triangle as sum of any two sides is greater then the third side.
iii) Possible to construct the triangle as sum of any two sides is greater then the third side.
iv) Not possible to construct a triangle as sum of
Question 3: In . Find
. Name i) the largest side of
, ii) the smallest side of
iii) write the sides of
in ascending order of their lengths.
Answer:
. Therefore
i) the largest side of
ii) the smallest side of
iii)
Question 4: In . Name i) the smallest side of
, ii) the largest side of
iii) write the sides of
in ascending order of their lengths.
Answer:
. Therefore
i) the largest side of
ii) the smallest side of
iii)
Question 5: In . Name the smallest side and the equal sides.
Answer:
Smallest side
Equal Sides
Question 6: In . Name the largest side and the equal sides.
Answer:
Largest side , Equal Sides
Question 7: In . Name the smallest side and the largest sides.
Answer:
Largest side , Smallest Side
Question 8: In the adjoining figure, . Find
. Also show that
Answer:
Therefore
Since
Since
Since
Question 9: In the adjoining figure, . If
, find the values of
.
Answer:
Since
(opposite angles)
Therefore
Which implies that
Becasue
Question 10: In the adjoining figure, . If
, find the value of
.
Answer:
Since
Therefore
Question 11: In the adjoining figure, and
. Show that
.
Answer:
Since
Since
Since
Since
Since
Question 12: If is a point on side
, prove that:
Answer:
In , because it is a valid triangle,
In , because it is a valid triangle,
In , because it is a valid triangle,
Add the above two relations
Question 13: In the adjoing figure, is a quadrilateral. Prove that: i)
ii)
iii)
iv)
Answer:
In
In
Adding the above two expresions we get
and
. Add these two expressions we get