This document summarizes a presentation given in India on the construction of an isosceles trapezium. It defines a trapezium as a quadrilateral with one set of parallel sides. An isosceles trapezium is then defined as a trapezium with congruent legs and base angles. The document discusses the Indian mathematician Baudhāyana and his contributions to geometry in the 800s BCE, including calculating pi and discovering the Pythagorean theorem. It then demonstrates how to construct an isosceles trapezium by drawing two parallel lines, finding the midpoint, and using a compass to draw arcs intersecting the parallel lines.

1. INDIA’S CONTRIBUTION
TO GEOMETRY
AT
BHIDE GIRLS’ HIGH SCHOOL, NAGPUR
1ST
& 2ND
DECEMBER, 2012

2. CONSTRUCTION OF ISOSCELES
TRAPEZIUM
Presented by-
Rishi Agrawal,
Head, Dept. of Mathematics,
Hislop College, Nagpur.
Tithi Agrawal,
Grade – 7,
Edify School, Nagpur.

3. TRAPEZIUM
(TRAPEZOID)
I have only one set of parallel
sides.
My median is parallel to the
bases and equal to one-half
the sum of the bases.

4. Isosceles Trapezoid
I have:
- only one set of parallel
sides
- base angles congruent
- legs congruent
- diagonals congruent
- opposite angles
supplementary
ISOSCELES TRAPEZOID

5. ISOSCELES TRAPEZIUM IN DAILY LIFE

6. Baudhāyana, (fl. c. 800 BCE) was
an Indian mathematician, who was most likely
also a priest. He is noted as the author of the
earliest Sulba Sūtra—appendices to the Vedas
giving rules for the construction of altars—
called the Baudhāyana Śulbasûtra, which
contained several important mathematical
results.

7. He is older than the other famous
mathematician Āpastambha. He belongs to
the Yajurveda school.
He is accredited with calculating the
value of pi before pythagoras, and with
discovering what is now known as
the Pythagorean theorem.

8. Baudhayana made the following constructions :
1)To draw a straight line at right angles to a given
straight line.
2)To draw a straight line at right angles to a given
straight line to a given point from it .
3)To construct a square having a given side.
4)To construct a rectangle of given sides.
5)To construct a isosceles trapezium of a given altitude,
face and base.

9. 6)To construct a parallelogram having given sides at a
given inclination.
7)To draw a square equivalent to n times a given square.
8)To draw a square equivalent to the sum of two
different squares.
9)To draw a square equivalent to two given triangles.
10)To transform a rectangle into square.

10. 11)To transform a square into rectangle.
12)To transform a square into an rectangle which shall
have an given side .
13)To transform a square or a rectangle into an triangle .
14)To transform a square into an rhombus.
15)To transform a rhombus into an square.

11. DRAWING ISOSCELES
TRAPEZIUM
• Draw two parallel line segments of
equal length, say AB and CD.
• Take P as midpoint of CD.
• Join PA and PB.
• Draw PM as altitude of ΔPAB.

12. • Consider a point Q on MP produced.
• With the center at M and radius MQ, draw an
arc of a circle, cutting line CD at points E and
F.
• Join AE and BF.
• AEFB is an isosceles trapezium.
DRAWING ISOSCELES
TRAPEZIUM

13. DRAWING ISOSCELES
TRAPEZIUM
Proof :
Δ APM and BPM are congruent.
Also ME = MF = radius of circle.
Therefore, Δ MEP are MFP are congruent.
=> Δ AEP and BFP are congruent.
=> AE = BF
Therefore, trapezium is isosceles with two non
parallel equal sides.

14. Thank U!!!