ABCD is a quadrilateral in which AD =BC and DAB=CBA prove that
(1) ABD = BAC
(2)BD =AC
(3) ABD = BAC
Answers
ANSWER
In △ABD and △BAC,
AD=BC (Given)
∠DAB=∠CBA (Given)
AB=BA (Common)
∴△ABD≅△BAC (By SAS congruence rule)
∴BD=AC (By CPCT)
And, ∠ABD=∠BAC (By CPCT)
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Answer:
Parallelogram
Parallelogram Properties
Properties of a parallelogram
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Adjacent angles are supplementary.
Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.
If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle.
Important formulas of parallelograms
Area = L * H
Perimeter = 2(L+B)
Rectangles
Rectangle Properties
Properties of a Rectangle
Opposite sides are parallel and congruent.
All angles are right.
The diagonals are congruent and bisect each other (divide each other equally).
Opposite angles formed at the point where diagonals meet are congruent.
A rectangle is a special type of parallelogram whose angles are right.
Important formulas for rectangles
If the length is L and breadth is B, then
Length of the diagonal of a rectangle = √(L2 + B2)
Area = L * B
Perimeter = 2(L+B)
Squares
Squares Properties
Properties of a square
All sides and angles are congruent.
Opposite sides are parallel to each other.
The diagonals are congruent.
The diagonals are perpendicular to and bisect each other.
A square is a special type of parallelogram whose all angles and sides are equal.
Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.
Important formulas for Squares
If ‘L’ is the length of the side of a square then length of the diagonal = L √2.
Area = L2.
Perimeter = 4L
Rhombus
Rhombus Properties
Properties of a Rhombus
All sides are congruent.
Opposite angles are congruent.
The diagonals are perpendicular to and bisect each other.
Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).
A rhombus is a parallelogram whose diagonals are perpendicular to each other.
Important formulas for a Rhombus
If a and b are the lengths of the diagonals of a rhombus,
Area = (a* b) / 2
Perimeter = 4L
Trapezium
Trapezium Properties
Properties of a Trapezium
The bases of the trapezium are parallel to each other (MN ⫽ OP).
No sides, angles and diagonals are congruent.
Important Formulas for a Trapezium
Area = (1/2) h (L+L2)
Perimeter = L + L1 + L2 + L3