# IGCSE Mathematics Paper-1: Specimen Questions with Answers 92 - 93 of 324

## Question 92

### Write in Short

Short Answer▾Factorize completely

### Explanation

Here,

Factoring is the decomposition of an object into a product of other objects or factors, which gives the original equation when multiplied together.So,

## Question 93

### Describe in Detail

Essay▾Diagram shows a triangle ABC and a rectangle ABDF. Angle and AB = 5 cm, AF = 9 cm and BC = 12.5 cm.

(a) (i) Write down the size of angle AEF.

(ii) Write down the size of angle BCA and EAF.

(b) Complete the statement: Triangle ABC is ________ to triangle AFE.

(c) AB = 5 cm, AF = 9 cm and BC = 12.5 cm. Calculate the length of EF.

### Explanation

(a) (i) Here, in angles BAC and AEF are alternate interior angles which will be similar.

So, .

(ii) For :

Here, both triangles are right-angled triangles, so

Now, in any triangle addition of all angles will be

So, in

So, in , will also be , as and are alternate interior angles.

(b) Here, Triangle ABC is **similar** to triangle AFE because there all three angles are same in both.

- Two triangles are called as
**congruent triangles**when both have all equal sides and equal angles. - Two triangles are called as
**similar triangles**:

o If all angles are same in both.

o If all pairs of sides are in same proportion.

o If two pairs of sides are in same proportion and one angle is also same in both.

(c) Here, AB = 5 cm, AF = 9 cm and BC = 12.5 cm are given,

So, formula for similar triangles for side: