**What is Geometry? **** **
**Geometry** is a subject in mathematics that focuses on the study of shapes, sizes, relative configurations, and spatial properties. Derived from the Greek word meaning “

*earth measurement*”, geometry is one of the oldest sciences. It was first formally organized by the Greek mathematician

**Euclid** around 300 BC when he arranged 465 geometric propositions into 13 books, titled ‘Elements’.

**What are Angle Properties, Postulates, and Theorems? **

In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems.

**Task 1:**

Define the following (& # 4, 6 & 8 post as a comment)

- Postulate
- Theorem
- Transversal
- Converse

*Nb: suggest you do a personal note or concept map to summarise the various types of geometrical properties.*
*The syllabus requires you to know the following:*
*Properties of angles eg. acute, reflect etc*
*Properties of angles and straight lines*
*Properties of angles between parallel lines*
*Properties of Triangle*

*courtesy of Lincoln Chu S1-02 2010*
*courtesy of Goh Jia Sheng S1-02 2010*
**Lets look at some of these Postulates **
**A. Corresponding Angles Postulate**
If a

__transversal__ intersects two

**parallel** lines, the pairs of corresponding
angles are congruent.

__Converse also true__: If a transversal intersects two lines and the corresponding
angles are congruent, then the lines are parallel.
*The figure above yields four pairs of corresponding angles.*

###
B. Parallel Postulate

Given a line and a point

__not__ on that line, there exists a unique line through the
point parallel to the given line.
The parallel postulate is what sets Euclidean geometry apart from

non-Euclidean geometry.

*There are an infinite number of lines that pass through point ***E**, but only
the red line runs parallel to line **CD**. Any other line through **E** will
eventually intersect line **CD**.

##
Angle Theorems

###
C. Alternate Exterior Angles Theorem

If a transversal intersects two

**parallel** lines, then the alternate exterior
angles are congruent.

__Converse also true__: If a transversal intersects two lines and the alternate
exterior angles are congruent, then the lines are parallel.
*The alternate exterior angles have the same degree measures because the lines are
parallel to each other.*

###
D. Alternate Interior Angles Theorem

If a transversal intersects two

**parallel** lines, then the alternate interior
angles are congruent.

__Converse also true__: If a transversal intersects two lines and the alternate
interior angles are congruent, then the lines are parallel.
*The alternate interior angles have the same degree measures because the lines are
parallel to each other.*

**E. Same-Side Interior Angles Theorem**
If a transversal intersects two

**parallel** lines, then the interior angles
on the same side of the transversal are supplementary.

*The sum of the degree measures of the same-side interior angles is 180°.*

###
F. Vertical Angles Theorem

If two angles are vertical angles, then they have equal measures.

*The vertical angles have equal degree measures. There are two pairs of vertical angles.*

**sources:**
**http://www.wyzant.com**

**http://www.mathsteacher.com.au/year9/ch13_geometry/05_deductive/geometry.htm **

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