Triangles and Similarity
Angle Sum Property of a Triangle
States that the sum of the interior angles of any triangle is always 180 degrees.
Area of a Triangle
Gives the area of a triangle given the length of any base and its corresponding altitude.
Midpoint Theorem
States that the segment connecting the midpoints of two sides of a triangle is parallel to and half the third side.
Basic Proportionality Theorem (Thales' Theorem)
States that a line drawn parallel to one side of a triangle divides the other two sides in the same ratio.
Converse of Basic Proportionality Theorem
States that if a line divides two sides of a triangle in the same ratio, it must be parallel to the third side.
Internal Angle Bisector Theorem
States that the internal bisector of an angle of a triangle divides the opposite side in the ratio of the containing sides.
AA Similarity Criterion
States that two triangles are similar if two pairs of corresponding angles are equal.
SSS Similarity Criterion
States that two triangles are similar if all three pairs of corresponding sides are in the same ratio.
SAS Similarity Criterion
States that two triangles are similar if two pairs of sides are proportional and their included angles are equal.
Corresponding Sides of Similar Triangles
States that the ratio of corresponding sides of two similar triangles is equal.
Corresponding Angles of Similar Triangles
States that all corresponding angles of two similar triangles are equal.
Ratio of Perimeters of Similar Triangles
Relates the ratio of perimeters of two similar triangles directly to the ratio of their corresponding sides.
Ratio of Areas of Similar Triangles
Relates the ratio of the areas of two similar triangles to the square of the ratio of their corresponding sides.
Pythagoras Theorem
States that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.