Geometry (Triangles (Angle Bisector
-Name of intersection pt. and…
Similarity of Triangles
-7 linear dimension ratio? (including median)
-Relationship bet. Sides and Area
-Difference between the congruent and similar triangle
-Two criteria to satisfy similarity of triangles
Triplets- 4 common triplets
-How to arrive at more triplets using above 4 basic triplets ?
-Triplets applied on inner triangle for an right angled triangle
Right Angled Triangle
-In Right angled triangle relation bet. mid point of hypo and vertices?
-(90-45-45) triangle relation bet hypo and base and altitude
-in (30-60-90) triangle relation bet hypo,altitude and base
-Definition, meeting point of medians
-Ratio in which centroid divides the median
-Number of medians required to find out centroid
-How medians divide the area of triangle?
1 median and all three median
-Name of intersection pt. and Definition
-Angle bisector theorem for sides
-Relation bet. angle made at center and at vertices
-Definition, meeting point
-Circumcenter position in a right angled triangle
-Difference wrt to altitude and orthocenter
-Relation bet. median, angle bisector and perpendicular bisector which falls on the unequal side
-Relation bet centroid, incentre, orthocentre, circumcentre
-Relation bet. median, angle bisector and perpendicular
-if side is "a" then altitude, area, circum-radius and incentre radius of the triangle
Line Joining the mid points
-line joining mid point are parallel wrt ?
-Length of line joining the mid points
-Area of triangle formed by joining mid points
Area of triangle
-Area using only sides
-Area using in radius and circum radius
-area using sides and included angle
-Use of cosine rule
formula, when to apply
- Area, Circumference, area of a sector, length of an arc from angle subtended, minor/major arc
- The perpendicular from center to the chord bisects it always and converse is also true.
- Equal chords are equidistant from the center
- Equal chords subtend equal angle at the center
- Relation bet. angle subtended by arc/chord at center and on circumference (this is for major segment)
- Relation bet. angle subtended for minor segment part of the circle.
- Sum of opposite angles property for cyclic quadrilateral
- Triangle formed with any chord is always isosceles as two sides will always be radius of equal lengths.
- What is the measure of the angle inscribed by the diameter on the arc of a semicircle?
- Definition, angle subtended by radius at tangent.
- Difference between tangents and secants.
- Length of two tangents originating from the same external point?
- Behaviour of line joining external point and center wrt to the angle between the two tangents?
- Relation bet. tangent and secant drawn on same circle
- Relation bet. two secants
Alternate segment theorem
- Definition, where to apply
- Relation bet. common chord and line joining the centers of two intersecting circles
- Unique case of orthogonally intersecting circles.
Lines and Angles
Transversal Line and all the angles associated
-BPT (Basic proportionality theorem)
- Definition in terms of sides and angles
- Angle subtended by each sides at center
- Sum of all angles of a regular polygon
- Measure of each of the angles of a regular polygon
- Properties of cyclic quadrilaterals
- Sum of all the angles in an quadrilateral
- Two properties of diagonals of squares
- Length of diagonal in square
- Diagonals of rectangle are equal and bisect
- Area of parallelogram
- Relationship between diagonal length and sides length.
- If all sides of parallelogram are equal then we get
- Diagonals of Rhombus are mutually perpendicular
- Area of rhombus = 1/2d1d2
- Are of trapezoid = 1/2 (b1+b2) height