CIE Mathematics Paper-1: Specimen Questions 93 - 93 of 175
Question number: 93
Describe in Detail
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.
(a) (i) Here, in angles BAC and AEF are alternate interior angles which will be similar.
(ii) For :
Here, both triangles are right-angled triangles, 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 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: