Thursday, June 18, 2009

Rules of Geometry for preparation of MBA entrance exams(CAT, XAT, FMS, MAT etc)

Rules of Geometry

- Two lines are said to be parallel only when their point of intersection is/are :

- In a triangle, 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 triangle, the sum of the 2 angles is equal to the third 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

- 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 altitude of a triangle with the side on which it is
drawn 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 regular 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 triangle formed by joining the mid points of the sides of an equilateral
triangle is : equilateral

- The bisectors of the angle at the vertex of an isosceles triangle: 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 :

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

- The point of intersection of the altitudes of the triangle is called :

- 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 equal 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 straight 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 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 quadrilateral bisect each other and are perpendicular, the quadrilateral is : rhombus

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

- If diagonals 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 quadrilateral are joined, 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 similar 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 rectangle 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 similar triangles formed is equal 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:

- 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 equal angles at the : center

- Angles in the same segment of a circle are : equal

- 2 Equal circles intersect in a and b. through 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 circle of radius r and distance b/w the centre of the
circle and any point r on a given line pr. the line doesn’t 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 subtended by the intercepted arc at the centre

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