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Congruence and Similarity

Secondary 2 practice

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Congruence and Similarity practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

△ABC ≡ △DEF. AB = 77 cm, BC = 44 cm, CA = 99 cm. Find the perimeter of △DEF.
7 cm4 cm9 cmABCDEFNot drawn to scale
Show the worked solution
  • △ABC≡△DEFgiven\triangle ABC \equiv \triangle DEF \quad \scriptsize\textit{given}
  • Congruent triangles have equal corresponding sides\text{Congruent triangles have equal corresponding sides}
  • DE=AB=7\text{DE} = \text{AB} = 7 cm, EF=BC=4\text{EF} = \text{BC} = 4 cm, FD=CA=9\text{FD} = \text{CA} = 9 cm
  • Perimeter of △DEF=7+4+9\text{Perimeter of }\triangle DEF = 7 + 4 + 9
  • =20= 20 cm

Answer: 2020

Example 2

In △ABC\triangle ABC, DD is a point on ABAB and EE is a point on ACAC. Given that △ADE\triangle ADE is similar to △ABC\triangle ABC, AD=5AD = 5 cm, DB=5DB = 5 cm and DE=6DE = 6 cm, find BCBC.
?DEDE = 6AD = 5DB = 5ABCNot drawn to scale
Show the worked solution
  • △ADE\triangle ADE is similar to △ABC\triangle ABC (given).
  • BCDE=ABADcorresponding sides in proportion\frac{BC}{DE} = \frac{AB}{AD} \quad \scriptsize\textit{corresponding sides in proportion}
  • AB=AD+DB=5+5=10AB = AD + DB = 5 + 5 = 10 cm
  • BC6=105\frac{BC}{6} = \frac{10}{5}
  • BC=6×105BC = 6 \times \frac{10}{5}
  • =6×2= 6 \times 2
  • =12= 12 cm

Answer: 1212

Example 3

A photograph measuring 77 cm by 77 cm is enlarged by a scale factor of 22. Find the area of the enlarged photograph in cm².
Show the worked solution
  • Original area=7×7=49\text{Original area} = 7 \times 7 = 49 cm²
  • Area scale factor=22=4area scale is square of length scale\text{Area scale factor} = 2^2 = 4 \quad \scriptsize\textit{area scale is square of length scale}
  • Enlarged area=original area×area scale factor\text{Enlarged area} = \text{original area} \times \text{area scale factor}
  • =49×4= 49 \times 4
  • =196= 196 cm²

Answer: 196196

Questions parents ask

Is it really free?

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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