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→Concept 1: Angles
==== Concept 1: Angles ====
==== Concept 1: Angles ====
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. angles can be classified according to the size of the angle.
===== Activities =====
===== Activities =====
====== [[Introducing formation of angle]] ======
====== [[Introducing formation of angle]] ======
The standard angle concept based on the relative inclination of two lines meeting at a point irrespective of length of arms is discussed in an exploratory method.
====== [[Types of angles]] ======
====== [[Types of angles]] ======
We will learn the following types of angles: right angles, acute angles, obtuse angles, straight angles, reflex angles and complete angle.
==== Concept 2: Pairs of angles ====
==== Concept 2: Pairs of angles ====
In geometry, certain pairs of angles can have special relationships. Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles and adjacent angles.
===== Activities =====
===== Activities =====
====== [[Adjacent angles]] ======
====== [[Adjacent angles]] ======
Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle.
====== [[Complementary angles]] ======
====== [[Complementary angles]] ======
Complementary angles are two angles with a sum of 90°. A common case is when they form a right angle.
====== [[Supplementary angles]] ======
====== [[Supplementary angles]] ======
Supplementary angles are two angles with a sum of 180°. A common case is when they lie on the same side of a straight line.
====== [[Vertically opposite angles]] ======
====== [[Vertically opposite angles]] ======
When two straight lines intersect each other four angles are formed.The pair of angles which lie on the opposite sides of the point of intersection are vertically opposite angles.
====== [[Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees|Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180<sup>o</sup>]] ======
====== [[Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees|Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180<sup>o</sup>]] ======
Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree
====== [[Linear pair axiom : If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line|Linear pair axiom : If the sum of two adjacent angles is 180<sup>o</sup>, then the non-common arms of the angles form a line]] ======
====== [[Linear pair axiom : If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line|Linear pair axiom : If the sum of two adjacent angles is 180<sup>o</sup>, then the non-common arms of the angles form a line]] ======
==== Concept 3: Parallel lines ====
==== Concept 3: Parallel lines ====
Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel.
===== Activities =====
===== Activities =====