This study notes consist of very important concept of Geometry. Students, we have seen in the recent exams of SSC-CGL PRE or Mains that the questions asked from geometry sections are directly based on these concepts. So just go through these notes and we will provide you a quiz which is strictly based on these concepts. For more such concept based notes follow us on a daily basis because from now we will provide it regularly-
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1. A centroid divides a median in 2 : 1 ratio.
Centroid a point of intersection of three medians.
2. Ratio of two adjacent sides of a triangle is equal to the two parts of third side which makes by the internal angle bisector.
3. In an equilateral triangle internal angle bisector and the median are same.4.
5. Any two of the four triangles formed by joining the mid-point of the sides of a given triangle are-congruent.
6. Two triangles have the same area if they have the same base and lie between two parallel lines.
7. In a triangle side opposite to smaller angle is smaller in comparison to the side which is opposite to greater angle.
8. Orthocenter → Point of intersection of three Altitudes.
Incentre → Point of intersection of the angle bisectors of a triangle
Circumcenter → Point of intersection of the perpendicular bisectors of the sides.
Median → Line joining the mid-point of a side to the vertex opposite to the side.
9. When the corresponding sides of two triangles are in proportion then the corresponding angles are also in proportion.
If the two triangles are similar, then we have the following results –
Ratio of area of two triangles = Ratio of squares of corresponding sides
Ratio of sides of two triangles= Ratio of height (Altitudes)
= Ratio of medians
= Ratio of angle bisector
= Ratio of in radii/circum radii
= Ratio of Perimeter
10. In a right angled triangle, the triangle on each side of the altitude drawn from the vertex of the right angle to the hypotenuse is similar to the original triangle and to each other too.