how to prove triangle congruent by ASA test
Answers
Answer:
Angle-Side-Angle (ASA) Rule
Angle-side-angle is a rule used to prove whether a given set of triangles are congruent.
The ASA rule states that:
If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
Angle-Angle-Side (AAS) Rule
Angle-side-angle is a rule used to prove whether a given set of triangles are congruent.
The AAS rule states that:
If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
In the diagrams below, if AC = QP, angle A = angle Q, and angle B = angle R, then triangle ABC is congruent to triangle QRP.
Three Ways To Prove Triangles Congruent
A video lesson on SAS, ASA and SSS.
SSS Postulate: If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.
SAS Postulate: If there exists a correspondence between the vertices of two triangles such that the two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
ASA Postulate: If there exits a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
