Question

State the similarity criterion for triangle .
Answer fast

Answer 1

AAA( all Three angles should be equal )

AAS( Two adjacent angles and one adjacent side should be equal )

Answer 2

1) AAA similarity : If two triangles are equiangular( all three angles are equal to each other), then they are similar.

Example : In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and ∠C= ∠F then ΔABC ~ ΔDEF by AAA criteria.

2) AA similarity : If two angles of one triangle are respectively equal to tow angles of another triangle, then the two triangles are similar.

Example : In ΔPQR and ΔDEF, ∠P = ∠D, ∠R = ∠F then ΔPQR ~ ΔDEF by AA criteria.

3) SSS similarity : If the corresponding sides of two triangles are proportional, then the two triangles are similar.

Example : In ΔXYZ and ΔLMN, XY = LM, YZ = MN and XZ = LN then 

ΔXYZ ~ ΔLMN by SSS criteria.

Two triangles XYZ and LMN such that 

XYLM=YZMN=XZLNXYLM=YZMN=XZLN Then the two triangles are similar by SSS similarity.

4) SAS similarity : If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.

In triangle ABC and DEF, ∠A = ∠D 

ABDE=ACDFABDE=ACDF

Then the two triangles ABC and DEF are similar by SAS.