Triangles Class 10 Notes Maths: Chapter 6
- Similar Figures : These are two geometrical figures having the same shape but not necessarily same size.
- Congruent Figures : Two figures that are similar in shape and size, are congruent to eachother.
- All congruent figures are similar but converse is not true.
- Thales’ Theorem or Basic Proportionality Theorem : If a line joining two sides of a triangle at distinct points (not necessarily the mid-points of both the sides) is parallel to the third side, then it divides both the sides in equal proportions.The Converse of Thales’
Theorem : If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.
- Mid-Point Theorem : The line joining the mid-points of two sides of a triangle is parallel to the third side and its length is equal to half of the length of the third side.
- Two triangles are considered to be similar if their corresponding angles are equal and their corresponding sides are proportional.
- If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
- The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides, the squares of the corresponding altitudes, the squares of the corresponding medians and the squares of the corresponding angle-bisector segments.
- two similar triangles have equal areas, then the two triangles are congruent.
- Pythagoras Theorem : The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides that contain the right-angle.
- Converse of Pythagoras Theorem : In a triangle, if the square of the longest side is equal to the sum of the squares of the other two sides, then the angle opposite to the longest side is a right-angle.