Similarity — Part 1: Similar figures and the conditions for similar triangles: visual lesson, ICSE Class 10 Mathematics

Lesson

Similarity, Part 1

Two figures are similar when they have the same shape, but not always the same size. In this part we learn to recognise similar triangles and to use them to find lengths.

In this lesson you will

Tell similar figures from congruent figures using equal angles and proportional sides
Write the correspondence of similar triangles and find the scale factor
Use the AA, SSS and SAS conditions (applied, not proved) to show that triangles are similar
Use similar triangles to find unknown lengths, as in shadow problems

Same shape, different size: matching angles equal.

Concept

What you will be able to do

Tell similar from congruent figures
Write the correspondence and find the scale factor
Use the AA, SSS and SAS conditions
Find unknown lengths, for example from shadows

Concept

Similar figures: same shape, different size

Two figures are similar when one is an enlargement or a reduction of the other. Matching angles are equal, and matching sides are in the same ratio $k$ , the scale factor.

Here $k = 2$ : every side of $\triangle PQR$ is twice the matching side of $\triangle ABC$
enlarging a figure never changes its angles

\dfrac{PQ}{AB} = \dfrac{QR}{BC} = \dfrac{RP}{CA} = k

Scale factor $k = 2$: $\dfrac{8}{4} = \dfrac{10}{5} = \dfrac{12}{6} = 2$. Lengths in cm.

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