Rules of Geometry
- Two lines are said to be parallel only when their point of intersection is/are :
none
- 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
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 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 :
isosceles
- 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 :
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 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:
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 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
No comments:
Post a Comment