Geometry (Basics) : Geometry (Basics)
An angle > than 180, but < 360 is called a reflex angle. : Two angles whose sum is 90 are called complementary angles.
Two angles having a sum of 180 are called supplementary angles. An angle > than 180, but < 360 is called a reflex angle.
When two lines intersect, two pairs of vertically opposite angles are equal. The sum of 2 adjacent angles is 180. : When two lines intersect, two pairs of vertically opposite angles are equal. The sum of 2 adjacent angles is 180.
If a cutting line cuts 2 parallel lines, then the corresponding angles r equal. : Alternate angles are equal.
Interior angles on the same side of the cutting line are supplementary. If a cutting line cuts 2 parallel lines, then the corresponding angles r equal.
Two lines are parallel to each other if : Two lines are parallel to each other if They r parallel to a 3rd line.
They r opposite sides of a rectangle or parallelogram.
If they r perpendicular to a 3rd line. If 1 of them is a side of & other joins midpoints of the remaining 2 sides.
If 1 of them is a side of a & other divides other 2 sides proportionately.
Slide 6 : 2 lines r perpendicular to each other if They r arms of a right-angle triangle.
If the adjacent angles formed by them r = & supplementary.
They r adjacent sides of a rectangle or a square. If they r diagonals of a rhombus.
If 1 of them is a tangent & other is radius of the circle through pt. of contact.
If the sum of their squares is = to the square of line joining their ends.
2 angles are said to be = if : They are vertically opposite angles.
Their arms are parallel to each other.
They are the corresponding angles of 2 congruent triangles.
They are the opposite angles of a parallelogram.
They are the angles of a equilateral triangle.
They are the angles of a regular polygon.
They are in same segment of a circle.
One of them lies between a tangent & a chord thorough the pt. of contact and other is in the alternate segment, in a circle. 2 angles are said to be = if
Two sides r = to each other if : They r corresponding sides of 2 congruents.
They r sides of an equilateral triangle.
They are opp. sides of a parallelogram.
They are the sides of a regular polygon.
They are radii of the same circles.
They are chords Equidistant from centre of circle.
They are tangents to a circle from an external point. Two sides r = to each other if
Two triangles r congruent : If 2 sides & the included angle of 1 triangle r respectively = to 2 sides & included angle of other triangle ( SAS).
If 2 angles & a side of one triangle r respectively congruent to 2 angles & the corresponding side of the other (AAS).
If 3 sides of 1 triangle r respectively congruent to 3 sides of the other (SSS).
If 1 side & hypotenuse of a right-triangle r respectively congruent to side & hypotenuse of other right triangle(RHS) Two triangles r congruent
Similarity of triangles : 2 triangles r similar if they alike in shape only. The corresponding angles are congruent,but corresponding sides are only proportional. All congruent triangles are similar but all similar triangles are not necessarily congruent. Similarity of triangles
Two triangles r similar if : 2 angles of one triangle are respectively equal to the 2 angles of the other triangle (AA).
2 sides of one triangle are proportional to 2 sides of the other & the included angles are equal.
All the three sides of one triangle are proportional to the three sides of the other triangle. Two triangles r similar if
Properties of similar triangles : If two triangles r similar, Ratios of sides=ratio of heights=ratio of medians=ratio of angle bisectors= ratio of inradii= ratio of circumradii.
Ratio of areas = b1h1/b2h2 = (s1)2/(s2)2 , where b1 & h1 r the base & height of triangle 1 & b2 & h2 r the base & height of triangle 2. S1 & s2 r the corresponding sides of triangle 1 & triangle 2 respectively. Properties of similar triangles