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Properties of Similar Triangles




Properties of Similar Triangles
Two triangles are said to be similar, if their
i) Corresponding angles are equal and
ii) Corresponding sides are proportional.



According to the figure.
ΔABC and ΔPQR are similar,
Since ∠ A = ∠P

∠B = ∠Q

∠C = ∠R

The symbol for “similar triangle is
~ .

Thus
ΔABC ~ ΔPQR

So corresponding sides are in proportion.

AB BC AC
----- = ------- = ------
PQ QR PR

Note : 1) Similar triangles are equiangular.
2) In similar triangles corresponding sides are proportional.
3) Congruent triangles are similar, but the converse is not always true.
4) Triangles similar to the same triangle are similar to each other.
5) Similar figures have the same shape, but not necessarily the same size.

If the corresponding sides are in proportion then the two triangles are similar.That means the converse is also true.
Practice


Q.1 Fill in the blanks.

1) Two triangles are similar,if their corresponding angles are ______.(proportional / equal )
(Ans)

2) Two polygons of the same number of sides are similar, if (a) their corresponding angles are ________ and (b) their corresponding sides are _________ ( equal , proportional,congruent)
(Ans)

Q.2 Write True Or False.

1) Any two figures are congruent.
(Ans)

2) Any two congruent figures are similar.
(Ans)

3) Two polygons are similar, if their corresponding sides are proportional.
(Ans)

Q.3 Similarity of two triangles are given, write the proportion of corresponding sides.
1) ΔABC
~ ΔPQR. (Ans)

2) ΔLMN
~ ΔDEF. (Ans)

3) ΔXYZ
~ ΔRAT. (Ans)
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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