Mark44 said:Why do you have four statements and five reasons? What does CPCTC stand for?
A congruence proof in geometry is a method of proving that two geometric figures, such as triangles or quadrilaterals, are exactly the same size and shape. This means that all corresponding sides and angles of the figures are equal.
The steps to prove congruence between two triangles are:
A congruence proof shows that two geometric figures are exactly the same size and shape, while a similarity proof shows that two figures have the same shape but may have different sizes. Congruent figures have all corresponding angles and sides equal, while similar figures have corresponding angles equal and corresponding sides in proportion.
Yes, congruence can be proven with just one pair of equal sides. This is known as the Side-Side-Side (SSS) congruence postulate. If two triangles have two pairs of equal sides, they are not necessarily congruent. However, if they also have one pair of equal angles, they are congruent by the Side-Angle-Side (SAS) congruence postulate.
You can determine if a set of figures is congruent by looking at them and checking if all corresponding sides and angles are equal. If two figures have the same size and shape, they are congruent. Additionally, if two figures are reflections or rotations of each other, they are also congruent.