4 Geometry 1 TERMINOLOGY
Altitude: Height. Any line segment from a vertex to the opposite side of a polygon that is perpendicular to that side
Polygon: General term for a many sided plane �gure. A closed plane (two dimensional) �gure with straight sides
Congruent triangles: Identical triangles that are the same shape and size. Corresponding sides and angles are equal. The symbol is /
Quadrilateral: A four-sided closed �gure such as a square, rectangle, trapezium etc.
Interval: Part of a line including the endpoints
Similar triangles: Triangles that are the same shape but different sizes. The symbol is zy
Median: A line segment that joins a vertex to the opposite side of a triangle that bisects that side
Vertex: The point where three planes meet. The corner of a �gure
Perpendicular: A line that is at right angles to another line. The symbol is =
Vertically opposite angles: Angles that are formed opposite each other when two lines intersect
Geometry try 1 Chapter 4 Geome
INTRODUCTION GEOMETRY IS USED IN many areas, including surveying, building and graphics.
These fields all require a knowledge of angles, parallel lines and so on, and how to measure them. In this chapter, you will study angles, parallel lines, triangles, types of quadrilaterals and general polygons. Many exercises in this chapter on geometry need you to prove something or give reasons for your answers. The solutions to geometry proofs only give one method, method, but other methods are also acceptable. acceptable.
DID YOU KNOW? Geometry means measurement of the earth and Geometry means earth and comes from Greek. Geometry was used in ancient civilisations such as Babylonia. However, it was the Greeks who formalised the study of geometry, in the period between 500 BC and AD 300.
Notation In order to show reasons for exercises, you must know how to name figures correctly. • B The point is called B.
The interval (part of a line) is called AB or BA.
If AB and CD are parallel lines, we write AB <
This angle is named
+ BAC
CD.
or +CAB. It can sometimes be named ^
Angles can also be written as BAC or BAC.
This triangle is named 3 ABC.
+ A
.
141
Geometry try 1 Chapter 4 Geome
INTRODUCTION GEOMETRY IS USED IN many areas, including surveying, building and graphics.
These fields all require a knowledge of angles, parallel lines and so on, and how to measure them. In this chapter, you will study angles, parallel lines, triangles, types of quadrilaterals and general polygons. Many exercises in this chapter on geometry need you to prove something or give reasons for your answers. The solutions to geometry proofs only give one method, method, but other methods are also acceptable. acceptable.
DID YOU KNOW? Geometry means measurement of the earth and Geometry means earth and comes from Greek. Geometry was used in ancient civilisations such as Babylonia. However, it was the Greeks who formalised the study of geometry, in the period between 500 BC and AD 300.
Notation In order to show reasons for exercises, you must know how to name figures correctly. • B The point is called B.
The interval (part of a line) is called AB or BA.
If AB and CD are parallel lines, we write AB <
This angle is named
+ BAC
CD.
or +CAB. It can sometimes be named ^
Angles can also be written as BAC or BAC.
This triangle is named 3 ABC.
+ A
.
141
142 14 2
Maths In Focus Mathematics Extension 1 Preliminary Course
To name a quadrilateral, go around it: for for example, BCDA is correct, but ACBD is not.
Producing a line is the same as extending it.
+ ABD
and
This quadrilateral is called ABCD called ABCD..
Line AB Line AB is is produced to C.
+DBC are
equal.
DB bisects DB bisects + ABC.
AM is is a median of D ABC.
AP is is an altitude of D ABC.
Types T ypes of Angles Acute angle
0c1 xc1 90c
