On this site you can practice at your own pace and at your own level. But beware: this does require responsibility! Make sure you practice enough, that you are sure that you have mastered the material and above all that you notify your teacher when you run into something.
If you need help with the material or planning, go to your teacher. Remember to always ask questions!
And always read the theory in your textbook!
You can work through this site independently (or when your teacher tells you to). It is important that you watch the video’s, read the extra theory carefully and practice well. Make the exercises from your book! You can find out which exercises you can complete here. Mathematics is something that you learn through practice and repetition!
On the left you can see the sidebar. The items in the sidebar are:
Planning: before you start, Look at the planner. Planning is important, without a plan you might end up not being able to finish all your work. You can read all about planning right here. The learning objectives per paragraph are also described here. After working through a paragraph, check whether you meet these learning objectives.
Prior knowledge: Here you can review what you need to know before starting this chapter.
Paragraphs: these sections are divided into:
Theory: often contains explanatory videos.
Extra theory: here the theory is explained again in text and examples. Make sure you read this!
Mock exam: This is a practice test. There is only 1 version so don't make it too early!
Make sure you work through all the paragraphs and get enough practice
This site was made for tto 1 based on getal & ruimte
Planning
You need to keep a planner to complete the chapter successfully. You can find a planner for this chapter here.
Mark exercises in the planner with:
a green marker to indicate that you found an exercise easy and which you did well.
an orange marker you to indicate that you found a problem difficult but that you solved it correctly.
a red marker to indicate that you have made a mistake.
If you find out that you have colored many problems red or orange, you may need extra practice. In this case, watch the videos again, go through the theory again and go to your teacher for help.
Keeping track of this planner and updating it, is important because this way you know exactly where you stand in your learning process. Another way to help you do this, is by keeping track of the learning objectives.
Always keep your own planner when doing schoolwork, make sure you do not set unrealistic goals such as “I am going to finish all my homework for math and Dutch today”. Try to set goals such as “I will concentrate on my math homework for half an hour, trying to complete x number of exercises”.
It is therefore important when planning your schoolwork you take into account the following.
How fast can I make the exercises?
How quickly do I understand new material?
How much guidance / help do I usually need?
What is a realistic amount of work that I can do?
If you encounter planning problems, discuss this with your mentor or teacher. They can help you with this.
7.1 Median and Altitude
Theory explained in text
A median of a triangle is the line segment that joins (runs from) any vertex of the triangle with the mid-point of its opposite side. In the figure shown below, the median from A meets the mid-point of the opposite side, BC, at point D. Make sure you mark the 2 halfs of the side with the same sign.
The properties of the medians: It cuts the triangle into smaller triangles that have the same area's (oppervlakte). It also cuts the side of the triangle into 2 line segments that have the same sides.
The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side).
An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle. Make sure you mark the perpendicular line with the sign of a right angle
An altitude of a triangle can be a side or may lie outside the triangle.
The orthocenter is the point where all three altitudes of the triangle intersect.
Different explanation, bit longer slower en more in depth:
7.2 Special triangles
Theory explained in text
Some triangles have special properties with makes them unique.
Isosceles triangle is a triangle with at two equal legs (sides). In triangle ABC given below, sides AB and AC are equal, and we call those legs. BC is the base.
The angles at the base are called the base angles and are the same
An equilateral triangle is a triangle with all three sides of equal length. It has 3 lines of symmetrie and has rotational symmetrie of 360o : 3 = 120o. The angles of a equailateral triangle are all 60o.
A right-angled triangle is a triangle in which one angle is a right angle (90o). Your protractor triangle is a right-angled triangle.
Theory explained in video's
Summary (watch until 5:05):
Isosceles triangle:
Equilateral triangle:
Right triangle:
7.3 Calculating angels in triangles
Theory explained in text
Make sure you know the sum of all the angles in a triangle, this is 180o.
You also need to know the following: With this information you can calculate the missing angles in an exercise. Sometimes it is nessesary to calculate other angles in a given figure before you can calculate the missing angle in the question.
Make sure you always make a sketch in your notebook you can use to help you!
It can help to just try and calculate as much as possible when your stuck and don't know how to proceed.
Remember to always write down in brackets why an angle is an certains amounts of degrees like in theory C (the image to the left)
Theory explained in video's
How to find the missing angle:
7.4 Special quadrilaterals
Theory explained in text
Make sure you know the properties of each of the following special quadrilaterals, you need to be able to recognize and draw each of these. Later you will need to be able to use these properties to solve math problems.
A parallelogram:
has point symmetrie
has opposites of the same length
has diagnonals that cut each other in half
has opposite angles that are equal
A rhombus:
has diagonals that for the axes of symmetry
has diagonals that intecest at an angle of 90o (perpendicular)
has diagonals that are bisectors of the angles
A rhombus is a special parallelogram, so the same properaties apply:
has point symmetrie
has opposites of the same length
has diagnonals that cut each other in half
has opposite angles that are equal
A trapezium:
has at least one pair opposite sites that are parallel.
A special trampezium called a isosceles trapezium:
also has two not parallel sides that are the same size.
This isosceles trapezium has one axis of symmetry
A kite:
has two pairs of equal adjacent sides
one pair of equal opposite angles
has diagonals that intersect at an 90o degree angle (perpendicular)
has at least one diangonal that is an axis of symmetry
Alternate angles.
When you have two parallel lines and a line that intersects with those you can see a Z shape. Like in the figure to the below:
Now If you have the Z shape in a figure (remember you have to have a set of parallel lines!) You can use the rule of alternate angles. Which is: Alternate angles are equal.
Here are some more examples of alternate angles and some non-examples:
Corresponding angles.
When you have two parallel lines and a line that intersects with those you can see a F shape. Like in the figure to the below:
Now If you have the F shape in a figure (remember you have to have a set of parallel lines!) You can use the rule of corresponding angles. Which is: Corresponding angles are equal.
Here are some more examples of corresponding angles and some non-examples:
Het arrangement Chapter 7 2D shapes is gemaakt met
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Auteur
Denise Norton
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Laatst gewijzigd
2022-04-18 10:34:57
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With this information you can calculate the missing angles in an exercise. Sometimes it is nessesary to calculate other angles in a given figure before you can calculate the missing angle in the question.
