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Congruence of Triangles
Two triangles are congruent if and only if one of them can be superimopse on the other, so as to cover it exactly.
The general condition for the congruence of two triangles is:
Two triangles are congruent if and only if there exists a corresponding between their vertices such that corresponding sides and the corresponding angles of the two triangles are equal.
SAS congruence Axiom i.e., Side Angle Side congruence Axiom
Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other.
In the figure given below, if AB is equal to EF, BC is equal to FG and angle B is equal to angle F, then triangle ABC is congruent to triangle EFG So. CA is equal to GE, angle A is equal to angle E, angle C is equal to angle G.
ASA i.e., Angle Side Angle congruence Axiom
Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.
In triangles ABC and PQR,
angle B is equal to angle Q, angle C is equal to angle R and BC is equal to QR.
Then, triangle ABC is congruent to triangle PQR and hence angle A is equal to angle P, AB is equal to PQ and AC is equal to PR.
SSS congruence Axiom
Two triangles are congruent if three sides of one triangle are equal to the corresponding three sides of the other triangle.
In triangles ABC is equal to DEF,
AB is equal to DE, BC is equal to EF and AC is equal to DF
Then triangle ABC is congruent to triangle DEF
Therefore, angle A is equal to angle D, angle B is equal to angle E and angle C is equal to angle F.
Right - Angled Hypotenuse Side congruence Axiom
Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.
Given that In triangles ABC and DEF,
angle B is equal to angle E is equal to 90 degrees, AC is equal to DF and BC is equal to EF
Triangle ABC is congruent to triangle DEF
Congruence of Triangles
Two triangles are congruent if and only if one of them can be superimopse on the other, so as to cover it exactly.
The general condition for the congruence of two triangles is:
Two triangles are congruent if and only if there exists a corresponding between their vertices such that corresponding sides and the corresponding angles of the two triangles are equal.
SAS congruence Axiom i.e., Side Angle Side congruence Axiom
Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other.
In the figure given below, if AB is equal to EF, BC is equal to FG and angle B is equal to angle F, then triangle ABC is congruent to triangle EFG So. CA is equal to GE, angle A is equal to angle E, angle C is equal to angle G.
ASA i.e., Angle Side Angle congruence Axiom
Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.
In triangles ABC and PQR,
angle B is equal to angle Q, angle C is equal to angle R and BC is equal to QR.
Then, triangle ABC is congruent to triangle PQR and hence angle A is equal to angle P, AB is equal to PQ and AC is equal to PR.
SSS congruence Axiom
Two triangles are congruent if three sides of one triangle are equal to the corresponding three sides of the other triangle.
In triangles ABC is equal to DEF,
AB is equal to DE, BC is equal to EF and AC is equal to DF
Then triangle ABC is congruent to triangle DEF
Therefore, angle A is equal to angle D, angle B is equal to angle E and angle C is equal to angle F.
Right - Angled Hypotenuse Side congruence Axiom
Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.
Given that In triangles ABC and DEF,
angle B is equal to angle E is equal to 90 degrees, AC is equal to DF and BC is equal to EF
Triangle ABC is congruent to triangle DEF
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