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:

Answer:

In

In

Adding the above two expresions we get

. Add these two expressions we get