Are similar and congruent triangles the same?
When triangles are similar, their angles are the same. But that does not mean that they have to be congruent. They can have the same angles but have sides of different lengths. So you can have two triangles where the angles are the same but where one has sides that are all 3 times the length of the other, for example.
When triangles are similar, their angles are the same. But that does not mean that they have to be congruent. They can have the same angles but have sides of different lengths. So you can have two triangles where the angles are the same but where
- When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
- A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°.
- Angle-Angle (AA) Similarity Postulate - If two angles of one triangle are congruent to two angles of another, then the triangles must be similar. 2. Side-Side-Side (SSS) Similarity Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar. 3.
AA (Angle-Angle) If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
- The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
- Two figures are similar if they have the same shape but not necessarily the same size. All of the figures below are congruent since they all have the same shape and size.
- In mathematics, a congruent transformation (or congruence transformation) is: Another term for an isometry; see congruence (geometry). A transformation of the form A → PTAP, where A and P are square matrices, P is invertible, and PT denotes the transpose of P; see Matrix Congruence and congruence in linear algebra.
Updated: 2nd October 2019