# 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

So corresponding sides are in proportion.

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.

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

2) ΔLMN

3) ΔXYZ

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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

• 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