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Grade 7 - Mathematics
Congruency of Triangles

Congruent Figures
  • Two plane figures are said to congruent if they have the same shape and same size.
  • Two line segments having the same length are congruent.

Congruent Triangles

There are four properties of congruency in triangles.

  1. 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.



  2. 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, B = E and C = F.
      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.

  3. 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.

  4. 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:
      B = E = 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.


Directions: Read the above review points carefully and answer the following questions:
  1. Illustrate each of the above properties by giving at least 5 examples.
  2. Explain in your own words the different properties of congruent triangles.
  3. Explain why there is no ASS property for congruent triangles.

Q 1: If three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.
SAS Property
RHS Property
SSS Property
ASA Property

Q 2: Two plane figures are said to be congruent if they have same size and same _____.
angle
shape
length

Q 3: 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.
SSS Property
SAS Property
RHS Property
ASA Property

Q 4: Two line segments having the same length are ______.
congruent
equal

Q 5: Two circles are congruent if they have the same ______.
arc
radius
center

Q 6: Two line segments are congruent if they have the same _____.
shape
length
area

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Question 8: This question is available to subscribers only!


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