CIE Mathematics Paper-1: Specimen Questions 93 - 93 of 175

Question number: 93

Essay Question▾

Describe in Detail

Diagram shows a triangle ABC and a rectangle ABDF. Angle BAC=750 and AB = 5 cm, AF = 9 cm and BC = 12.5 cm.

A triangle and Rectangle set into each other

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 ABCandAFE angles BAC and AEF are alternate interior angles which will be similar.

So, AEF=750 .

(ii) For BCAandEAF :

Here, both triangles are right-angled triangles, so ABCandAFEwillbeof900.

Now, in any triangle addition of all angles will be 1800.

So, in ABC, ABC+BCA+BAC=1800

900+BCA+750.=1800

BCA+1650=1800

BCA=18001650

BCA=150

So, in AFE , EAF will also be 150 , as EAF and BCA 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: ABEF=BCAF5EF=12.59EF=5×912.5EF=3.6cm.

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