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 : (2n4)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
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