Triangle (2) - Congruence and Similarity

 

*** CONGRUENCE ***

Two triangles are CONGRUENT when they have the exact same size and shape and could be placed so as to coincide perfectly.

Triangle are congruent if any one of the following is true:

• The three sides of △ ABC are equal to the three corresponding sides of the other triangle △ DEF

• Two sides and the angle between those sides (the 'included' angle) of △ ABC  are equal to the corresponding parts of the other triangle △ DEF

• Two angles and one side of one triangle △ ABC are equal to the corresponding parts of the other triangle △ DEF

• Two right-angled triangles are congruent if the hypotenuse and a leg of one triangle △ ABC are equal to the corresponding sides of the second triangle △ DEF

The symbol for congruence is ≅  e.g. △ ABC ≅ △ DEF

Further material - University of Texas - Triangle Congruence

 

*** SIMILARITY ***

Similarity tells us that two triangles have the same shape but not necessarily the same size. The corresponding angles of similar triangles are equal but not the corresponding sides.

Triangles are similar if:

Two angles of one triangle △ ABC are equal to to angles of the other triangle △ DEF

Three sides of one triangle △ ABC are proportional to the three sides of the other triangle △ DEF

Two sides of one triangle △ ABC are proportional to two sides of the other triangle △ DEF and the angles between those two sides are equal 

The symbol for similarity is ~  e.g.  △ ABC ~ △ DEF

Further material - University of Texas - Similarity

 

The two triangles are similar. What is the length of x.

The ratio is 4 to 12 or 1 to 3. Hence, the x = 21 cms - that is 3 x 7

Additional material

Maths is Fun - Similar Triangles

Third Space Learning - Congruence and similarity