Similarity and congruenceIB MYP Maths Extended: Subtopic test

1. 1
   Triangle $ABC$ has $AB=7$ cm, $BC=9$ cm and $CA=6$ cm. Triangle $DEF$ has $DE=6$ cm, $EF=7$ cm and $FD=9$ cm.

   (a)

   Which condition shows that triangle $ABC$ is congruent to triangle $DEF$?

   [1 mark]

   • AAAA
   • BSSS
   • CSAS
   • DRHS

   (b)

   Which angle in triangle $DEF$ is equal to angle $ABC$?

   [1 mark]

   • A$E\hat{D}F$
   • B$D\hat{E}F$
   • CNone of them, because the triangles are not congruent
   • D$D\hat{F}E$

   (c)

   A pupil says: 'Any two triangles with the same three angles must be congruent.' Explain why the pupil is wrong, giving an example.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two rectangles are similar. The smaller rectangle is $6$ cm long and $4$ cm wide. The larger rectangle is $15$ cm long.

   (a)

   Find the scale factor of the enlargement from the smaller rectangle to the larger rectangle.

   [1 mark]

   • A$2.5$
   • B$9$
   • C$0.4$
   • D$6.25$

   (b)

   Find the width of the larger rectangle.

   [1 mark]

   • A$13$ cm
   • B$1.6$ cm
   • C$10$ cm
   • D$25$ cm

   (c)

   Find the area scale factor from the smaller rectangle to the larger rectangle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A model car is made to a scale of $1:25$ of a real car. The real car is $4.5$ m long.

   (a)

   Find the length of the model car in centimetres.

   [3 marks]

   (b)

   The real car has a windscreen with an area of $1.5$ m$^2$. Find the area of the windscreen on the model, in cm$^2$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company sells two similar bottles of water. The small bottle is $20$ cm tall and holds $500$ mL. The large bottle is $30$ cm tall. The label on the small bottle has an area of $150$ cm$^2$.

   (a)

   (i) Find the length scale factor from the small bottle to the large bottle.
   (ii) Find the volume of the large bottle in mL.
   (iii) Both labels are similar. Find the area of the label on the large bottle.

   [6 marks]

   (b)

   The small bottle sells for AED $3.00$ and the large bottle for AED $8.50$. An advert says: 'The large bottle is only $50\%$ taller, so it holds only $50\%$ more water.' Use your volume from part (a) to compare the price of the two bottles per $100$ mL, decide which is better value, and evaluate the claim in the advert.

   [6 marks]

   Total for question 4: 12 marks

End of questions