Quadrilaterals - General Geometry Mathematics Notes | EduRev

Additional Topics for IIT JAM Mathematics

Mathematics : Quadrilaterals - General Geometry Mathematics Notes | EduRev

The document Quadrilaterals - General Geometry Mathematics Notes | EduRev is a part of the Mathematics Course Additional Topics for IIT JAM Mathematics.
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Angles
It is common knowledge that the sum of the angles in a triangle is 180° but how about in polygons with a greater numbers of angles? If we are given a convex polygon with n sides and S is the sum of the measures of the interior angles then S = 180(n - 2).
Example
Find the sum of the measures of the interior angles in an octagon.
The octagon has 8 sides and we plug this value into our formula:
S = 180(8 - 2) = 1080°
Hence the sum of the measures of the interior angles in an octagon is 1080°.
Another thing with convex polygons is that the sum of the measures of the exterior angles is always 360°
Quadrilaterals - General Geometry Mathematics Notes | EduRev
m∠A + m∠B + m∠C + m∠D + m∠E + m∠F = 360

Properties of parallelograms
One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.
Quadrilaterals - General Geometry Mathematics Notes | EduRev
There are six important properties of parallelograms to know:
1. Opposite sides are congruent (AB = DC).
2. Opposite angels are congruent (D = B).
3. Consecutive angles are supplementary (A + D = 180°).
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent triangles.
Quadrilaterals - General Geometry Mathematics Notes | EduRev
△ACD ≅ △ABC
If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi.
If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs. If the legs are congruent we have what is called an isosceles trapezoid.
Quadrilaterals - General Geometry Mathematics Notes | EduRev
In an isosceles trapezoid the diagonals are always congruent. The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases.
Quadrilaterals - General Geometry Mathematics Notes | EduRev
Quadrilaterals - General Geometry Mathematics Notes | EduRev

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