Home
Siyavula textbooks: grade 10
Geometry basics
Polygons
Other polygons
There are many other polygons, some of which are given in the table below.
Sides
Name
5
pentagon
6
hexagon
7
heptagon
8
octagon
10
decagon
15
pentadecagon
Table of some polygons and their number of sides.
Examples of other polygons.
Angles of regular polygons
You can calculate the size of the interior angle of a regular polygon by using:
A
^
=
n
-
2
n
×
180
∘
where
n is the number of sides and
A
^ is any angle.
Areas of polygons
Area of triangle:
1
2
× base
× perpendicular height
Area of trapezium:
1
2
× (sum of
∥ (parallel) sides)
× perpendicular height
Area of parallelogram and rhombus: base
× perpendicular height
Area of rectangle: length
× breadth
Area of square: length of side
× length of side
Area of circle:
π x radius
2
Khan academy video on area and perimeter
Khan academy video on area of a circle
Polygons
For each case below, say whether the statement is true or false. For false statements, give a counter-example to prove it:
All squares are rectangles
All rectangles are squares
All pentagons are similar
All equilateral triangles are similar
All pentagons are congruent
All equilateral triangles are congruent
Find the areas of each of the given figures - remember area is measured in square units (cm
2 , m
2 , mm
2 ).
Summary
Make sure you know what: quadrilaterals, vertices, sides, angles, parallel lines, perpendicular lines,diagonals, bisectors and transversals mean.
Similarities and differences between quadrilaterals
Properties of triangles and quadrilaterals
Congruency of triangles
Classification of angles into acute, right, obtuse, straight, reflex or revolution
Theorem of Pythagoras which is used to calculate the lengths of sides of a right-angled triangle
Angles:
Acute angle: An angle 0 and 90
Right angle: An angle measuring 90
Obtuse angle: An angle 90 and 180
Straight angle: An angle measuring 180◦
Reflex angle: An angle 180 and 360
Revolution: An angle measuring 360
Angle properties and names
Equilateral, isoceles, right-angled, scalene triangles
Triangles angles = 180
Congruent and similar triangles
Pythagoras
Trapezium, parm, rectangle, square, rhombus, kite and properties
Areas of particular figures
Exercises
Find all the pairs of parallel lines in the following figures, giving reasons in each case.
Find angles
a ,
b ,
c and
d in each case, giving reasons.
Which of the following claims are true? Give a counter-example for those that are incorrect.
All equilateral triangles are similar.
All regular quadrilaterals are similar.
In any
▵
A
B
C
with
∠
A
B
C
=
90
∘ we have
A
B
3
+
B
C
3
=
C
A
3 .
All right-angled isosceles triangles with perimeter 10 cm are congruent.
All rectangles with the same area are similar.
Say which of the following pairs of triangles are congruent with reasons.
For each pair of figures state whether they are similar or not. Give reasons.
Challenge problem
Using the figure below, show that the sum of the three angles in a triangle is 180
∘ . Line
D
E
is parallel to
B
C .
Questions & Answers
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
Google Play and the Google Play logo are trademarks of Google Inc.