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 || 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