Triangles+-+Bec

= Chapter 4 =  Triangles, Quadrilaterals and Constructions!

This is exam revision for chapter 4 in the 'Essential Mathhematics VELS Edition for Year 7'. Chapter 4 is all about triangles, quadrilaterals and constructions. I hope that this page is useful for your upcoming exam, as a lot of hard work and effort has gone into creating it! Let's get studying!

//__4.1 - Naming and measuring angles __//
What is an angle? An angle is formed when two lines (called arms) meet at a point known as the vertix.

Angle sizes
= **__// QUIZ TIME! //__ ** = How big are these angles? 1.  2.  3. 
 * Angle type || <span style="font-family: Georgia,serif; font-size: 16px;">Angle Size || <span style="font-family: Georgia,serif; font-size: 16px;">Example ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Acute Angle || <span style="font-family: Georgia,serif; font-size: 16px;">Between 0 and 90 degrees || <span style="font-family: Georgia,serif;">[[image:http://www.glogster.com/media/2/9/58/45/9584546.gif width="158" height="92"]] ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Right Angle || <span style="font-family: Georgia,serif; font-size: 16px;">Exactly 90 degreesYou will know if something has/is a rightangle, as there will be a box, instead of a circular shape || <span style="font-family: Georgia,serif;">[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Right_angle.svg/134px-Right_angle.svg.png width="82" height="92"]] ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Straight Angle || <span style="font-family: Georgia,serif; font-size: 16px;">Exactly 180 degrees || <span style="font-family: Georgia,serif;">[[image:math8geometry/straightangle.jpg width="167" height="61"]] ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Obtuse Angle || <span style="font-family: Georgia,serif; font-size: 16px;">Any size between 90 and 180 degrees || <span style="font-family: Georgia,serif;">[[image:http://www.freehomeworkmathhelp.com/Geometry/Geometry_Introduction/geometry_homework_help_obtuse_angle.GIF width="199" height="117"]] ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Reflex Angle || <span style="font-family: Georgia,serif; font-size: 16px;">Any size between 180 and 360 degrees || <span style="font-family: Georgia,serif;">[[image:http://www.maths.com/angles/reflexangle.jpeg width="136" height="80"]] ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Circular Angle/ perigon/ Revolution || <span style="font-family: Georgia,serif; font-size: 16px;">One complete turn || <span style="font-family: Georgia,serif;">[[image:http://www.mathsisfun.com/definitions/images/angle-360.gif width="89" height="100"]] ||

<span style="font-family: Georgia,serif;">Anwsers: <span style="font-family: Georgia,serif;">1 - 120 Degrees <span style="font-family: Georgia,serif;">2 - 100 Degrees <span style="font-family: Georgia,serif;">3 - 30 Degrees

__//<span style="font-family: Georgia,serif;">4.2 - Scalene, Equilateral and Isosceles Triangles //__
<span style="font-family: Georgia,serif; font-size: 16px;">What is a triangle?

<span style="font-family: Georgia,serif; font-size: 16px;">A triangle is a three sided shape, which every line meets another at a vertix. Differently shaped triangles have different names. Angles are classified by the property of their sides.

<span style="font-family: 'arial black',gadget,sans-serif; font-size: 16px;">Different Triangles -

 * <span style="font-family: Georgia,serif; font-size: 16px;">Name || <span style="font-family: Georgia,serif; font-size: 16px;">Shape || <span style="font-family: Georgia,serif; font-size: 16px;">Number of equal sides || <span style="font-family: Georgia,serif; font-size: 16px;">Number of equal angles ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Equilateral Triangle || <span style="font-family: Georgia,serif;">[[image:http://mathworld.wolfram.com/images/eps-gif/EquilateralTriangle_1000.gif width="85" height="88"]] || <span style="font-family: Georgia,serif; font-size: 16px;">3 || <span style="font-family: Georgia,serif; font-size: 16px;">3 - Each angle must be the same, and every side must be the same ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Isosceles Triangle || <span style="font-family: Georgia,serif;">[[image:http://4.bp.blogspot.com/_mpEYMpxkyS8/S-7V0fTyZRI/AAAAAAAABHI/MMI5tuOS6Kc/s1600/tri.gif width="107" height="162"]] || <span style="font-family: Georgia,serif; font-size: 16px;">2 || <span style="font-family: Georgia,serif; font-size: 16px;">2 - Two angles must be the same, as do two sides, the third angle/side must be different to the others ||
 * <span style="font-family: Georgia,serif; font-size: 16px;">Scalene Triangle || <span style="font-family: Georgia,serif;">[[image:http://www.mathatube.com/images/f-407-1-1.gif width="139" height="143"]] || <span style="font-family: Georgia,serif; font-size: 16px;">0 || <span style="font-family: Georgia,serif; font-size: 16px;">0 - Every angle/side must be different. If any sides are the same it isn't Scalene ||

= **<span style="font-family: Georgia,serif;">__// QUIZ TIME! //__ ** = <span style="font-family: Georgia,serif; font-size: 130%;">Classify each of the following angles <span style="font-family: Georgia,serif; font-size: 130%;">1. <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">2. <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">3. <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">Answers: <span style="font-family: Georgia,serif;">1 - Scalene <span style="font-family: Georgia,serif;">2 - Equilateral <span style="font-family: Georgia,serif;">3 - Isoceles

<span style="color: #8521ed; font-family: Georgia,serif;">//__4.3 - Right-Angled, Acute Angled and Obtuse Angled Triangles__//
<span style="font-family: Georgia,serif;">Triangles can be classified by the size of their angles.

<span style="font-family: Georgia,serif;">If every angle in the triangle is acute, then it can be classified an acute-angled triangle - <span style="font-family: Georgia,serif;">

<span style="font-family: Georgia,serif;">If the triangle has one right angle, then it can be classified a right-angled triangle -

<span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">If the triangle has one obtuse angle, then it can be classified as an obutse-angled triangle - <span style="font-family: Georgia,serif;">

= **<span style="font-family: Georgia,serif;">__// QUIZ TIME! //__ ** = <span style="font-family: Georgia,serif; font-size: 130%;">Please classify the following triangles:

<span style="font-family: Georgia,serif; font-size: 130%;">1. <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">2. <span style="font-family: Georgia,serif;">

<span style="font-family: Georgia,serif;">3. <span style="font-family: Georgia,serif;"> <span style="font-family: 'Georgia','serif'; font-size: 13px;">Answers - <span style="font-family: 'Georgia','serif'; font-size: 13px;">1: Acute-angled Angle <span style="font-family: 'Georgia','serif'; font-size: 13px;">2: Obtuse-angled triangle <span style="font-family: 'Georgia','serif'; font-size: 13px;">3: Right-angled triangle

__//<span style="font-family: 'Georgia','serif'; font-size: 13px;">4.4 - Drawing triangles given a combination of sides and angles //__
<span style="font-family: 'Georgia','serif'; font-size: 13px;">To draw any triangle, you don't have to know the lengths of all the sides and sizes of angles. But you do need some information, which is called 'sufficient information'. There are three different ways that information can be given to you and you can determind the shape/size of the triangle:

<span style="font-family: 'Georgia','serif'; font-size: 13px;">1 - The lengths of two sides and the angle between them <span style="font-family: 'Georgia','serif'; font-size: 13px;">2 - The leghts of all three sides and no angles <span style="font-family: 'Georgia','serif'; font-size: 13px;">3 - The length of one side and the angles at each end

__//<span style="font-family: 'Georgia','serif'; font-size: 13px;">4.5 - Quadrilaterals and parallelograms //__
<span style="font-family: Georgia,serif;">What are quadrilaterals and parallelograms? <span style="font-family: 'Georgia','serif'; font-size: 13px;"> Every four sided shapes are called quadrilaterals. Similar to triangles, quadrilaterals are classified according to their shape and size.

= = =<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 13px;">Quadrilaterals/Parallelograms =
 * <span style="font-family: Georgia,serif;">Name || <span style="font-family: Georgia,serif;">Shape || <span style="font-family: Georgia,serif;">Special Properties ||
 * <span style="font-family: Georgia,serif;">Parallelogram || <span style="font-family: Georgia,serif;">[[image:http://www.ies.co.jp/math/products/geo1/applets/para/para1.gif width="175" height="119"]] || <span style="font-family: Georgia,serif;">A parallelogram is quadrilateral,with both pairs of opposite sides that are parallel. This shape has two pairs of equal sides and angles. ||
 * <span style="font-family: Georgia,serif;">Rhombus/diamond || <span style="font-family: Georgia,serif;">[[image:http://thesaurus.maths.org/mmkb/media/png/Rhombus.png width="149" height="194"]] || <span style="font-family: Georgia,serif;">A rhombus/diamond is a parallelogram with 4 equal sides, 2 pairs of equal angles and 2 pairs of parallel sides. ||
 * <span style="font-family: Georgia,serif;">Rectangle || <span style="font-family: Georgia,serif;">[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rectangle_example.svg/250px-Rectangle_example.svg.png width="125" height="63"]] || <span style="font-family: Georgia,serif;">A rectangle is a parallelogram with each angle 90 degrees. ||
 * <span style="font-family: Georgia,serif;">Square || <span style="font-family: Georgia,serif;">[[image:http://3.bp.blogspot.com/-4oAWWCcNNz4/Tjr3nKNyVUI/AAAAAAAAPLU/Pouua-pNsEY/s1600/sq.gif width="134" height="131"]] || <span style="font-family: Georgia,serif;">A square is a parallelogram with 4 equal sides and4 equal angles all 90 degrees. ||
 * <span style="font-family: Georgia,serif;">Trapezium || [[image:http://1.bp.blogspot.com/_8x59qeaRG28/S77cDETE6FI/AAAAAAAAACc/kI54pTgSbMg/s400/trapezium.png width="207" height="169"]] || <span style="font-family: Georgia,serif;">A trapezium is a quadrilateral with one pair of opposite sides parallel. ||
 * <span style="font-family: Georgia,serif;">Kite || <span style="font-family: Georgia,serif;">[[image:http://thesaurus.maths.org/mmkb/media/png/Kite.png width="167" height="180"]] || <span style="font-family: Georgia,serif;">A kite is a quadrilateral with two pairs of equal adjacent sides (adjacent means beside each other)or one pair of opposite angles equal. ||

= //**__<span style="font-family: 'Georgia','serif';">QUIZ TIME! __**// =

<span style="font-family: 'Georgia','serif';">Name each of the following quadrilaterals/paralellogram: <span style="font-family: Georgia,serif;">1 <span style="font-family: Georgia,serif;">

<span style="font-family: Georgia,serif;">2 <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">3 <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">Answers: <span style="font-family: Georgia,serif;">1 - rectangle <span style="font-family: Georgia,serif;">2 - Rhombus/diamond <span style="font-family: Georgia,serif;">3 - Square