**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?**

**Task 1:**

- 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**

Postulate -Postulate is a true statement, which does not require to be proved.

ReplyDeleteTheorem-A theorem is a math term used to describe an idea that can be proved.

Transversal-A line that cuts across two or more (usually parallel) lines.

Converse-if-Statement in which the hypothesis and the conclusion are switched.

good definition - where is the source?

ReplyDeletePostulate - a true statement that does not need prove

ReplyDeletehttp://www.icoachmath.com/math_dictionary/postulate.html

Theorem - a mathematical statement which can be proved with given set of assumptions

http://www.thefreedictionary.com/theorem

Transversal - a line that cuts across two or more (usually parallel) lines.

http://www.mathopenref.com/transversal.html

Converse - a theorem whose hypothesis and conclusion are the conclusion and hypothesis of another.

source : apple dictionary

Very impressive blog, and I am here to share something about triangle as -The similar triangles are also called as equiangular triangle. This is because in equilateral triangles, both the triangles have equal angles. The similar triangles have common shape but different sizes.

ReplyDelete