CIE Mathematics Paper-1: Specimen Questions with Answers 58 - 58 of 175

Question number: 58

Essay Question▾

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°.

Two parallel lines and two intersecting lines

Two Parallel Lines and Two Intersecting Lines

Find the below given calculations by using appropriate formulas and methods

(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.

Explanation

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

So, .

(ii) For :

Here, is given, 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 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: