ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------------------

Q2. State giving reasons, whether the following pairs of triangles are congruent or Not.

Answer

Congruent by ASA

Answer

Answer

ASA Theorem applied, Triangles are Congruent.

Answer

Applying Pythagoras theorem,

Hence Triangles are congruent by SAS

Q3. In the adjoining figure, P in the mid point of AB and . Prove that:

Answer:

, (given)

(given)

(opposite angles)

Hence

Q4. In the adjoining figure, . Prove that

Answer

Given

Therefore, by ASA

Q5. In the adjoining figure,

Answer

In

and DA = CB

Therefore, by ASA,

Q6. In the adjoining figure, ABC is a triangle in which .

Answer

Take

is common and

Therefore, by ASA,

Q7.

Answer

By SSS,

Therefore

Q8. In , it in given that in bisector of , meeting BC at D. Prove: i)

Answer

(angles opposite equal sides of a triangle)

(angle bisector)

Therefore by ASA:

Hence

Q9. In the adjoining figure, in such that . Prove that:

Answer

Given

Therefore,

AB = AC (given)

AO is Common

Because

Therefore, SAS applies, Hence

Since

Q10. In the adjoining figure,

Answer

In

(alternate angles)

(alternate angles)

Hence,

Given is common.

Therefore,

Applying ASA,

Q11. In the adjoining figure, ABCD as a square and CEB is an isosceles triangle in which EC = EB show:

Answer

Given (Sides of a square)

(Sides of an isosceles triangle)

Hence SAS applies,

Therefore,

Q12. Find the vales of x and y in each of the following cases:

Answers

i)

Given

(alternate angles)

Therefore, AAS applies Hence,

Therefore

ii)

In

Therefore by SSS,

Hence,

iii)

In

And PQ in common

Therefore, by SSS,

Hence

Therefore

Since,

Now Calculate,

iv)

In

Hence, ASA applies, Therefore,

Hence

And

Q13. In adjoining figure, the sides BA and CA of have been produced to D and E such that BA = AD and CA = AE Prove ED ∥ BC

Answer

In

(Opposite Angles)

Hence

Hence

Q14. Equilateral triangle ABC and ACE have been drawn on the sides AB and AC respectively of , as shown in the adjoining figure, prove: i)

Answer

In

Hence Therefore,

Q15. In a regular pentagon ABCDE, prove that is isosceles.

Answer

Since ABCD in a regular pentagon, all sides are equal and all internal angles are .

In

Therefore

Hence Therefore, isosceles triangle

Q16. In the adjoining figure, in a square, and are points on the side respectively such that,

Answer

Given ABCD in a square

(given)

Similarly

Now Consider

(Square)

Q17. In the adjoining figure,

Answer:

Since

And Similarly,

Given

Therefore, using AAS,

Q18. In the adjoining figure ABCD is a square, , and R is mid point of EF. Prove:

Answer

In ,

(Median would bisect the angle)

Common

In

(Side of a square)

(Proved above)

Because

Applying SAS, Proves that

Therefore, . Hence Proven.

Q19. In the adjoining figure, in the Mid point of PQ Prove:

Answer

In

(given)

(given)

Since

Q20. In adjoining figure,

Answer

Consider

is common

(given)

Hence,

Therefore,

Now Consider

is common

Therefore,