Introduction to congruence:
Two objects are congruent if they consist of the similar shape with size. The given two triangles are congruent if their equivalent sides are equal within length also their equivalent angles are the same in size. Assume the triangles DEF and RST is congruent. These can be written as ? DEF ? ? RST. In geometry two congruent triangles contains the equal corresponding angles.
Example of Congruence
The followings are the important congruence test
ASA congruence
The two angles with the integrated faces of one triangle are equal to the corresponding two angles with the integrated faces of another triangle.
SAS congruence
The two faces with the included angle of triangle are the same to two faces with the included angle of another triangle.
AAS congruence
The two angles along throughout a non integrated side of one triangle are congruent to the identical measurements of a different triangle.
SSS congruence
Three sides of one triangle are identical to corresponding three sides of another triangle.
Example
Consider the following two triangles.
The triangle IJK is congruent to the triangle LMN
Angle I = Angle L
Angle J = Angle M
Angle K = Angle N
Length IJ = Length LM
Length JK = Length MN
Length KI = Length LN
Understanding how do you simplify fractions is always challenging for me but thanks to all math help websites to help me out.
Examples for Congruence
Example 1 for congruence
In the following triangles are congruent then find the length of sides a, b, c.
Solution
The given triangles are congruent. Therefore the lengths of the sides of the triangles are equal.
Length EG = 52
Therefore the length VT = a = 52
Length FG = 48
Therefore the length UT = b = 48
Length EF = 50
Therefore the length UV = c = 50
Thus the a = 52, b = 48, c = 50.
Example 2 for congruence
Prove that triangle LMN is congruent to triangle PQR.
Solution
Given figure the angle L and angle P are the same.
Angle L = Angle P = 75 degree
Given figure the angle N and angle Q are the same.
Angle N = Angle Q = 65 degree.
Line segment LM is equal to the line segment PR.
Line LM = Line PR = 40 cm.
Therefore ? LMN and ? PQR are congruent through AAS congruence.
Two objects are congruent if they consist of the similar shape with size. The given two triangles are congruent if their equivalent sides are equal within length also their equivalent angles are the same in size. Assume the triangles DEF and RST is congruent. These can be written as ? DEF ? ? RST. In geometry two congruent triangles contains the equal corresponding angles.
Example of Congruence
The followings are the important congruence test
ASA congruence
The two angles with the integrated faces of one triangle are equal to the corresponding two angles with the integrated faces of another triangle.
SAS congruence
The two faces with the included angle of triangle are the same to two faces with the included angle of another triangle.
AAS congruence
The two angles along throughout a non integrated side of one triangle are congruent to the identical measurements of a different triangle.
SSS congruence
Three sides of one triangle are identical to corresponding three sides of another triangle.
Example
Consider the following two triangles.
The triangle IJK is congruent to the triangle LMN
Angle I = Angle L
Angle J = Angle M
Angle K = Angle N
Length IJ = Length LM
Length JK = Length MN
Length KI = Length LN
Understanding how do you simplify fractions is always challenging for me but thanks to all math help websites to help me out.
Examples for Congruence
Example 1 for congruence
In the following triangles are congruent then find the length of sides a, b, c.
Solution
The given triangles are congruent. Therefore the lengths of the sides of the triangles are equal.
Length EG = 52
Therefore the length VT = a = 52
Length FG = 48
Therefore the length UT = b = 48
Length EF = 50
Therefore the length UV = c = 50
Thus the a = 52, b = 48, c = 50.
Example 2 for congruence
Prove that triangle LMN is congruent to triangle PQR.
Solution
Given figure the angle L and angle P are the same.
Angle L = Angle P = 75 degree
Given figure the angle N and angle Q are the same.
Angle N = Angle Q = 65 degree.
Line segment LM is equal to the line segment PR.
Line LM = Line PR = 40 cm.
Therefore ? LMN and ? PQR are congruent through AAS congruence.
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