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
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