Similarity in Geometry

In this section we will discuss similarity in Geometry.

Two geometric figures having the same shape and size are known as congruent figures. Note that congruent figures are same in all respect.

Geometric figures having the same shape but different sizes are known as similar figures.
To represent a similar figure we use ~ this sign .

For example, if triangle ABC and triangle PQR are similar then it can be represented as follows .
Δ ABC ~ ΔPQR.

Examples :

1) Any two line segments are always similar but they need not be congruent. They are congruent if their lengths are equal.


2) Any two equilateral triangles are similar.



3) Any two circles are similar but not necessarily congruent. They are congruent if their radii are equal.


There is always one-to-one correspondence between the parts of two similar figures.

Practice


Q.1 Fill in the blanks.

1) All circles are _________ (congruent / similar). (Ans)

2) All _________ triangles are similar.(isosceles / equilateral). (Ans)

3) All square are ________( similar / congruent). (Ans)

Q.2 How many similar triangles are there in the figure?


(Ans)

Q.3 Identify the pair having similar triangles.


(Ans)

Q.4 Give two different examples of pair of

(i) Similar Figures (Ans-i)
(ii) Non-similar figures (Ans-ii)

Q.5 State the similarity or not :
(i) The two circles with radii 4cm and 5cm.
(ii) Two equilateral triangles with sides 5cm and 8cm each.
(iii) Two triangles, one is right triangle and other is isosceles triangle.
Similarity in Triangles

• Similarity in Geometry
• Properties of similar triangles
• Basic Proportionality Theorem(Thales theorem)
• Converse of Basic Proportionality Theorem
• Interior Angle Bisector Theorem
• Exterior Angle Bisector Theorem
• Proofs on Basic Proportionality
• Criteria of Similarity of Triangles
• Geometric Mean of Similar Triangles
• Areas of Two Similar Triangles

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