CIE Mathematics Paper-1: Specimen Questions 57 - 58 of 175
Question number: 57
Write in Short
- Factoring is the decomposition of an object into a product of other objects or factors, which gives the original equation when multiplied together.
Question number: 58
Describe in Detail
In the diagram, the lines AB and CD are parallel. The lines AD and BC intersect at X. Angle XDC = 35° and angle CXD = 120°.
(a) (i) Write down the size of angle BAX.
(ii) Write down the size of angle ABX
(b) Complete the statement: Triangle AXB is ________ to triangle DXC.
(c) AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm. Calculate the length of CX.
(a) (i) Here, in angles BAX and CDX are alternate interior angles which will be similar.
(ii) For :
Here, is given, so .
Now, in any triangle addition of all angles will be
So, in , will also be , as and are alternate interior angles
(b) Here, Triangle AXB is similar to triangle DXC 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 = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm are given,
So, formula for similar triangles for side: