2. Each pair of alternate interior angles are equal: ∠3 = ∠6, ∠4 = ∠5 3. Each pair of interior angles on the same side of the transversal are supplementary: ∠3+∠5=180; ∠4+∠6=180

1. MEASURING ANGLE 2. SQUARE IT

CORRESPONDING ANGLES ALTERNATE INERIOR ANGLES ALTERNATE EXTERIOR ANGLES SAME SIDE INTERIOR ANGLES:

The motive for mathematical investigation in early times has been social needs, commercial and financial transactions, calendar reckoning, navigation, construction of bridges, churches etc. Intellectual curiosity, a zest for pure thought and search for beauty, led to pursuit of properties of numbers and geometric figures. The study of geometry is helpful in all forms of art, architecture, engineering, physics, chemistry, medicine etc. Though Geometry has been in the civilization of man from very early times, it was developed significantly by the Egyptians,Babylonians and Greeks. Later all concepts were unified by Euclid in his book called “ Elements”. It is true that all geometric concepts arise from and represent definite physical objects. For example, a stretched rope represents a line but the Greeks made all these concepts abstract. For instance, the colour and material of the rope is not under consideration when you think of a line. The advantage is generality, so that the ideas are permanent and perfect. They did not realise or foresee the uses of their investigation which came much later. There is no perfect straight line, circle or spheres in nature. So Euclid abstracted all the ideas by starting with some undefined terms and truths which were accepted unquestionably. We will now see how our environment offers insights into the abstract concepts described in the Euclidian Geometry. POINT: The sharp tip of a thorn gives an idea of a point which has no parts, but has only a position, without dimensions. LINE SEGMENT: The branch of a tree, a shoot of bamboo suggest a line segment that lies evenly between it’s ends. It is also the shortest route from one end to the other. RAY: A ray is a line which starts at one point and goes endlessly in one direction. LINE: A line segment extending endlessly in both directions ( to be imagined). Here we explain the concept of infinity. It is larger than the largest that we can think of. We can think about God’s Grace which is infinite. INTERSECTING LINES: Intersecting Lines - Two lines passing through a common point. PARALLEL LINES: Parallel Lines – They don’t meet CURVE: The above is an example of a Curve SIMPLE CLOSED CURVE: The boundary of this lake ( marked in yellow) is a simple closed curve. The boat ( encircled in red) is in the interior of the curve. The tree ( encircled in red) is in the exterior of the curve. POLYGON: Polygon is a simple closed figure made up of line segments The centre point of these 3 leaves when joined gives a triangle ( 3 sides)