Scale Drawings & Similar Figures • Topic 1 of 2

Identifying Similar Polygons

Similar figures have the same shape but may differ in size.

Two conditions for similarity:

  1. All corresponding angles must be EQUAL
  2. All corresponding sides must be PROPORTIONAL (same scale factor k)

For triangles, if two angles match (AA rule), the triangles are automatically similar.

CheckSimilar?
Rectangles 4x6 and 8x12Yes: ratios 8/4=2 and 12/6=2 are equal
Triangles 30-60-90 and 30-70-80No: second angles differ (60 vs 70)
Any two squaresYes: all angles 90deg, sides always proportional
SIMILAR TRIANGLES:

Triangle A (small)     Triangle B (large)
      C (50 deg)               C' (50 deg)
      /\                          /\
     /  \                        /  \
    / 60  \ 70               / 60  \ 70
   /________\               /________\
  A   8cm   B             A'   16cm   B'

Scale factor = 16/8 = 2
All corresponding angles equal: A=A', B=B', C=C'
Solved Examples
1
Worked Example
Are rectangles with sides 4cm x 6cm and 8cm x 12cm similar?
SolutionRatio of widths: 8/4=2. Ratio of lengths: 12/6=2. Both ratios are equal, so YES they are similar with scale factor 2.
2
Worked Example
A triangle has angles 30, 60, 90. Another has angles 30, 70, 80. Are they similar?
SolutionNO — corresponding angles do not all match (60 != 70 and 90 != 80).

Key Points

  • Similar = same shape, different size
  • All corresponding angles must be equal
  • All side length ratios must equal the same scale factor k
  • For triangles: if 2 angles match (AA), automatically similar
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.Similar polygons have the same shape but not necessarily the same:
Explanation: Size may differ.
Q2.In similar polygons, corresponding angles are:
Explanation: Equal.
Q3.In similar polygons, corresponding sides are:
Explanation: Proportional.
Q4.The symbol for similarity is:
Explanation: $\sim$.
Practice more MCQs → 📝 Assignment · 35 marks