One thing we learnt in today's tutorial was to use the properties of congruent triangles.
Triangles are said to congruent if they have the same shape and same size.
Congruent Triangles
There are four properties of congruency in triangles.
- The SAS Property:
If two sides and the included angle of a triangle are respectively equal to two sides and the included angle of another triangle, then the two triangles are congruent.
- Let us consider two triangles ABC and DEF.
Conditions:
If AB = DE, BC = EF and the included angle BAC = the included angle EDF.
If the above conditions are satisfied, then we say that the two triangles ABC and DEF are congruent and we can write it as ABC @ DEF.
This is called Side, Angle, Side property.
- Let us consider two triangles ABC and DEF.
- The ASA Property:
If two angles and a side of one triangle are respectively equal to two angles and the corresponding side of another triangle, then the two triangles are congruent.
- Let us consider two triangles ABC and DEF.
Conditions:
If BC = EF, ÐB = ÐE and ÐC = ÐF.
If the above conditions are satisfies then we say that the two triangles ABC and DEF are congruent and we can write it as ABC @ DEF.
This is called Angle, Side, Angle property.
- Let us consider two triangles ABC and DEF.
- The SSS Property:
If three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.
- Let us consider two triangles ABC and DEF.
Conditions:
If AB = DE, BC = EF AND AC = DF.
If the above conditions are satisfies then we say that the two triangles ABC and DEF are congruent and we can write it as ABC @ DEF.
This is called Side, Side, Side property.
- Let us consider two triangles ABC and DEF.
- The RHS Property:
If the hypotenuse and a side of a right-angled triangle are equal to the hypotenuse and a side of another right-angled triangle, then the two triangles are congruent.
- Let us consider two triangles ABC and DEF.
Conditions:
ÐB = ÐE = 90°, side BC = Side EF and hypotenuse AC = hypotenuse DF. If the above conditions are satisfies then we say that the two triangles ABC and DEF are congruent and we can write it as ABC @ DEF.
This is called the Right Angle, Hypotenuse, Side property.
- Let us consider two triangles ABC and DEF.
Reference:
http://www.kwiznet.com/p/takeQuiz.php?ChapterID=2817&CurriculumID=24
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