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 triangle and Rectangle set into each other
Find the below given calculations by using appropriate formulas and methods
(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: