Points To Remember : Important Points to Remember in Geometry

Rules of Geometry

- Two lines are said to be parallel only when their point of intersection is/are : none

- In a triange, interior opposite angle is always less than : the exterior angle.

- Sum of the 2 interior opposite angles of a triangle is always equal to :

exterior angle

- Sum of all the interior angles of a pentagon is equal to : 540

- In a traingle, the sum of the 2 angles is equal to the thrid angle, considering interior angles only, then the triangle is : right angled

- Sum of the interior angles of a polygon having n sides is equal to : (2n-4)90

degrees

- 2 sides of a triangle are unequal. the angle just opposite to the larger side is : greater than the angle opposite the smaller side

- The angle made by the altitute of a triangle with the side on which it is drwan is equal to : 90 degrees

- One angle of a triangle is greater than the other. the side opposite to it is : greater than the side opposite to the other.

- Sum of squares on 2 perpendicular sides of a right angled triangle is equal to the square on the : hypotenuse

- In a parallelogram, the opposite angles are : equal.

- A regualr hexagon has been inscribed in a circle. the area of the hexagon will be: less than the area of the circle.

- When the bisector of any angle is perpendicular to the opposite side, then the triangle is : equilateral.

- If 2 parallel lines are intersected by a traversal, then the bisectors of the interior angels so formed make a : rectangle.

- Each angle of a complementary set of angles must be : acute.

- Number of pairs of vertical angles formed when 2 lines intersect are : 2.

- If the bisectors of 2 adjacent angles are perpendicular, the adjacent angles are the angles of : linear pair.

- The traingle formed by joining the mid points of the sides of an equilateral traingle is : equilateral.

- The bisectors of the angle at the vertex of an isosceles traingle: bisects the base and is perpendicular to it.

- If 2 angles of a triangle are congruent, the sides opposite of these angles are : congruent

- If the bisector of any angle of a triangle bisects its opposite side, the triangle is : isosceles.

- The correct postulate of congruence of 2 triangles is : SAS.

- The straight line joining the midpoints of any 2 sides of a triangle is : parallel to the third side

- if the bisector of the vertical angle bisects the base, the triangle is : isosceles.

- the point of intersection of the medians of the triangle is called : centroid.

- the point of intersection of the altitudes of the trianlgle is called : orthocentre

- in a triangle abc, if the median BE is equal to the median CF, then the triangle is : isosceles

- in a triangle ABC, if altitude BE is euqal to the altitude CF, then the triangle is : isosceles

- the angle between the internal bisector of one base angle and the exterior bisector of the other base angle is equal to : one half the vertical angle

- the bisector of the exterior angle at the vertex of an isosceles triangle is : parallel to the base

- the stright line drawn from the midpoint of a side of a triangle, parallel to the base is one that : bisects the other side

- the median on the hypotenuse of a right angled triangle is equal to : nothing can be said

- in an an isosceles triangle ABC, d,e,f are the midpoints of the base BC and the equal sides AB, AC resp, then : DF=DE

- medians of a triangle pass thru the same point which divides each median in the ratio : 2:1

- the sum of 2 medians of triangle is : greater than the third.

 - a median divides a triangle into 2 triangles of : equal area

- a triangle can have at most one : obtuse angle

- if the diagonal of a quadilateral bisect each other and are perpendicular, the quadilateral is : rhombus

- the bisector of a pair of opposite angles of a 11gm are : intersecting at a point

- if diagnols AC = diagonal BD and AC is perpendicular to BD in a parallelogram ABCD then it is : rhombus

- area of s rectangle and area of || gm standing on the same base and b/w the same || have relation b/w them as : they are equal

- if the midpoints of the sides of a quadilateral are jonied, then the figure formed is : ||gm

- if the diagonals of a || are equal then its a : rectangle

- a diagonal of a |\gm divides it into : 4 triangles of equal area

- in a triangle ABC, the median AD bisecting the side BC has its midpoint O.

the line CO meets AB at E. AE is equal to : AB/3

- if a line is drawn || to 1 side of a triangle, the other 2 sides are divided : in

the same ratio

- if the diagonals of a ||gm are equal, its a : rectangle

- AAA theorem is applicable for 2 triangles to prove them : similar

- the ratios of areas of similiar triangles is equal to the ratio of : squares on the corresponding sides

- if 2 chords of a circle intersect inside or outside a circle, the rectangle contained by the parts of 1 chord is equal in area to the rectange contained by : the parts of the other

- if the perpendicular drawn from the vertex of a right angled triangle to the hypotenuse, the number of similiar triangles formed is euqal to : 3

- in triangle abc, ad is perpendicular to bc. if ad^2 = bd*dc, the triangle is : right angled.

- in a ||gm abcd, e is a pt on ad. ac and be intersect each other at f. then: bf*fa=ef*fc.

- p and q are 2 pts on the sides ca and cb of a triangle abc, right angled at c. then aq^2 + bp^2 is equal to : ab^2 + pq^2

- equal chords of a circle subtends euqal angles at the : center

- angles in the same segment of a cirlce are : equal

- 2 equal circles intersect in a and b. thruogh b is a straight line perpendicular to ab drawn to meet the circumference in x and y. then : ax=ay - p is the centre of a cirlce of radius r and distance b/w the centre of the circle and ne point r on a given line pr. the line doesnt intersect the circle when : pr>r

- chord pq of a circle is produced to o. t is a pt such that ot becomes a tangent to the circle. then : ot^2=op*oq

- p is the midpoint of an arc apb of a circle. the tangent at p is : parallel to the chord ab.

- an angle with vertex on the circle formed by secant ray and a tangent ray has measure equal to : half the measure of the angle subtented by the intercepted arc at the centre