Triangle congruency means two triangles are identical in shape and size, where their corresponding sides and angles are equal.
What is the SAS (Side-Angle-Side) congruency criteria?
SAS states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Describe the ASA (Angle-Side-Angle) criteria for congruency.
ASA states that two triangles are congruent if two angles and the side between those angles in one triangle are equal to two angles and the corresponding side in another triangle.
What is the RHS (Right angle-Hypotenuse-Side) congruency criterion?
RHS says that two right-angled triangles are congruent if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle.
Explain the AAS (Angle-Angle-Side) congruency criterion.
AAS states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
What is meant by the SSS (Side-Side-Side) congruency criterion?
SSS states that if all three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.
How many criteria are there for triangle congruency?
There are five criteria for triangle congruency: SSS, SAS, ASA, AAS, and RHS.
Does SSA (Side-Side-Angle) prove triangle congruency?
No, SSA does not definitively prove triangle congruency because it does not always result in congruence.
Can congruent triangles have different areas?
No, congruent triangles have the same area because they are identical in shape and size.
What is the significance of congruent triangles in geometry?
Congruent triangles are used in proofs and constructions as they allow the application of properties of one triangle to another.
What must be true about corresponding sides in congruent triangles?
Corresponding sides in congruent triangles must be equal in length.
Why can't SSA be considered a congruency criterion?
SSA is not a reliable criterion because the same side lengths can produce different triangle shapes (ambiguous cases).
How does the ASA criterion ensure both congruency of angles and sides?
ASA establishes congruency by ensuring two angles and the included side are identical, leaving no other shape permutation possible.
What happens if two triangles fulfill the SSS criterion?
If two triangles fulfill the SSS criterion, they are congruent because all their corresponding sides are equal.
Does the presence of a right angle in two triangles guarantee their congruency?
Not by itself, but with equal length of the hypotenuse and one other side (RHS), congruency is ensured.