Question

How many criteria are there for similarity of triangles? Name them.

Answer 1

Heya !!

Before mentioning the criteria for similarity of triangles, Let's have a quick look at Rules and criteria for congruence of triangles.

Here we go !!

Rules for congruency of Triangles.

1. SSS (Side Side Side): Two triangles are congruent if all the three sides of one triangle are equal to the corresponding three sides of the other triangle.

2. SAS (Side Angle Side): Two triangles are congruent if two sides and the inclusive angle of one triangle are equal to the corresponding two sides and inclusive angles of the other triangle.

3. ASA (Angle Side Angle): Two triangles are congruent if its two angles and inclusive side is equal to the corresponding two angles and the inclusive side of the other triangle.

4. RHS (Right-angle Hypotenuse Side{Either Base or Height}): Two triangles are congruent if their hypotenuse and either base or height are equal to one another.

Criteria for congruency of Triangles.

There is only one criteria for congruency of triangles, ie, AngleAngleSide Congruence Criteria.

According to it, if two angles and exclusive side of one triangle are equal to the corresponding two angles and exclusive side of the other triangle, they are congruent by AAS .

Criteria for Similarity of Triangles.

1. SSS Criteria: Two triangles are similar if their sides are proportionate.

2. SAS Criteria: Two triangles are similar if their two sides are proportionate and the inclusive angles of both triangles are equal in magnitude.

3. AA or AAA Criteria: If two angles of two triangles are equal, the the third angles automatically becomes equal. Two triangles are similar if two (or all three) of their angles are equal in magnitude.

Hope it helps !!

Answer 2

Answer :


Q: What is Similarity ?
Ans :- Two figures are said to be congruent, if they have the same shape and same size. But the figures of the same shape need not have the same size. The figures of the same shape, but not necessarily of the same size are called similar figures.


Two polygons are said to be similar to each other, if :

1. Their corresponding angles are equal, and

2. The lengths of their corresponding sides are proportional.

Note '∼' is the symbol used for 'is similar to'.



There are three criteria for similarity of triangles :-

1) If ∠A = ∠D, ∠B = ∠E and ∠C = ∠F, then ∆ABC ∼∆DEF. This property is called AAA criterion.

2) If AB/DE = BC/EF = AC/DF, then ∆ABC ∼∆DEF. This property is called SSS criterion.

3) If AB/DE = AC/DF and ∠A = ∠D, then ∆ABC ∼∆DEF. This property is called SSS criterion.