Geometry Constructions
Axioms : The self-evident truths or the basic facts which are accepted without any proof are called axioms.
Types of Angles
Reflex Angle : An angle whose measure is more than 180o and less than 360o is called a reflex angle.
Theorem on Geometrical Figure Lines
If two lines intersect, then the vertically opposite angles are congruent.
Parallel Lines
Two lines are parallel if they are coplanar and they do not intersect each other even if they are extended on either side.
Transversal of Lines
A transversal is a line that intersects (or cuts) two or more coplanar lines at distinct points.
Theorem on Alternate angles.
If a transversal intersects two parallel lines, then each pair of alternate angles are equal.
Converse of Theorem on Alternate angles
If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are parallel.
Theorem on Supplementary Angles
If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.
Converse of Theorem on Supplementary Angles
If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
Interior Angles of a Triangle
In a triangle when we refer to an angle, we mean the angle bounded by the two sides. The three angles lie in the interior region of the triangle. These angles are called the interior angles of the triangle.
Theorem on Interior Angles and Exterior Angles of a Triangle
If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles.
Angle Sum Property of a Triangle
A triangle is a plane closed geometric figure formed by three line segments joining three non-collinear points.
Triangle Sum Theorem
The sum of the three angles of a triangle is 180o.
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