Maths

❤💘💗💖💕💓 Maths💝💞💟💙💚💛💜 

In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point. A bearing is used to represent the direction of one point relative to another point. For example, the bearing of A from B is 065º. The bearing of a point is the line joining the centre of the compass through the point measured in degrees in a clockwise way from the north direction. In navigation, bearings are used to express something about direction. It is also used to express in angle a particular landmark. c.It is written in 3-digit angles. The bearing of a point is the line joining the centre of the compass through the point measured in degrees in a clockwise way from the north direction. In navigation, bearings are used to express something about direction. It is also used to express in angle a particular landmark. c.It is written in 3-digit angles.Bearings are always three figures, and are always measured clockwise from north. Bearings. A bearing is an angle, measured clockwise from the north direction. Below, the bearing of B from A is 025 degrees (note 3 figures are always given).

Facts From Books

Facts From Books

• For over a hundred years cycling has been an exciting way of covering distances at High Speed.
• The New York Yankees have won the world series 27 times. That is the most of any team.
• Early baseball bats come in many shapes and sizes.
• Umpires help to run a baseball game.
• pro baseball games have nine innings. The longest game went for 26 innings.
• A runner must touch all of the bases before scoring.
• There's a lot of string in a baseball.
• Some players made their own bats.
• Some bats were long and skinny others were short some were even flat.
• They call balls and strikes they also decide where their base runners are safe or out.
• If a game is tied it's time for extra innings the longest game went for 26 innings.
• If you miss a base and are tagged with the ball your out.
• If you stretched it out it would be more than 1,000 feet (305 meters) long.

Textiles

In Textiles we have been learning about each other and other stuff such as Paint+Stencil which we have done for the last 2 lessons and we have been continuing our slide called Culturally Me that our teacher Mrs. Laycock shared with us. She is a really nice teacher.

Maths at School

Maths at school.

In Maths we have been learning about Prisms.

Prisms are A solid object with two identical ends and flat sides. The shape of the ends gives the prism a name, such as the Triangular Prism shown here. There are also Square Prisms, Pentagonal Prisms, and more. The cross-section is the same all along its length.

English-Creative Writing

English-Creative Writing 

In English, we have been doing creative writing a couple of weeks before we went into lockdown. This is what we have been doing ever since we came back to school.

Art

In Art, we have been doing kahui birds = drawing them, cutting it out, and printmaking. I have made up a slide for you to look at.

     

Learning Angle Rules For Maths Using GeoGebra

Angle Rules For Maths Using GeoGebra

For the past couple of weeks in maths, we have been learning about angle rules on GeoGebra.

Line segment: A line segment has two endpoints with a definite length.

Ray: A ray has one endpoint and infinitely extends in one direction.

Straight-line: A straight line has neither start nor endpoint and is of infinite length.



Acute angle: The angle that is between 0° and 90° is an acute angle, ∠A in the figure below.

Obtuse angle: The angle that is between 90° and 180° is an obtuse angle, ∠B as shown below.

Right angle: The angle that is 90° is a Right angle, ∠C as shown below.

Straight angle: The angle that is 180° is a straight angle, ∠AOB in the figure below.

Supplementary angles:

In the figure above, ∠AOC + ∠COB = ∠AOB = 180°

If the sum of two angles is 180° then the angles are called supplementary angles.

Two right angles always supplement each other.

The pair of adjacent angles whose sum is a straight angle is called a linear pair.

Complementary angles:

∠COA + ∠AOB = 90°

If the sum of two angles is 90° then the two angles are called complementary angles.

Adjacent angles:

The angles that have a common arm and a common vertex are called adjacent angles.

In the figure above, ∠BOA and ∠AOC are adjacent angles. Their common arm is OA and the common vertex is ‘O’.

Vertically opposite angles:

When two lines intersect, the angles formed opposite to each other at the point of intersection (vertex) are called vertically opposite angles.

In the figure above,

x and y are two intersecting lines.

∠A and ∠C make one pair of vertically opposite angles and

∠B and ∠D make another pair of vertically opposite angles.

Perpendicular lines: When there is a right angle between two lines, the lines are said to be perpendicular to each other.

Here, the lines OA and OB are said to be perpendicular to each other.

Parallel lines:

Here, A and B are two parallel lines, intersected by a line p.

The line p is called a transversal, which intersects two or more lines (not necessarily parallel lines) at distinct points.

As seen in the figure above, when a transversal intersects two lines, 8 angles are formed.

Let us consider the details in a tabular form for easy reference.

Types of Angles	Angles
Interior Angles	∠3, ∠4, ∠5, ∠6
Exterior Angles	∠1, ∠2, ∠7, ∠8
Vertically opposite Angles	(∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)
Corresponding Angles	(∠1, ∠5), (∠2, ∠6), (∠3, ∠7), (∠4, ∠8)
Interior Alternate Angles	(∠3, ∠5), (∠4, ∠6)
Exterior Alternate Angles	(∠1, ∠7), (∠2, ∠8)
Interior Angles on the same side of the transversal	(∠3, ∠6), (∠4, ∠5)

When a transversal intersects two parallel lines,

1. The corresponding angles are equal.
2. The vertically opposite angles are equal.
3. The alternate interior angles are equal.
4. The alternate exterior angles are equal.
5. The pair of interior angles on the same side of the transversal is supplementary.

We can say that the lines are parallel if we can verify at least one of the aforementioned conditions.

Let us take a look at some examples.

Solved examples

Example 1. If the lines m and n are parallel to each other, then determine the angles ∠5 and ∠7.

Solution:

Determining one pair can make it possible to find all the other angles. The following is one of the many ways to solve this question.

∠2 = 125°

∠2 = ∠4 since they are vertically opposite angles.

Therefore, ∠4 = 125°

∠4 is one of the interior angles on the same side of the transversal.

Therefore, ∠4 + ∠5 = 180°

125 + ∠5 = 180 → ∠5 = 180 – 125 = 55°

∠5 = ∠7 since vertically opposite angles.

Therefore, ∠5 = ∠7 = 55°

Note: Sometimes, the parallel property of the lines may not be mentioned in the problem statement and the lines may seem to be parallel to each other; but they maybe not. It is important to determine whether two lines are parallel by verifying the angles and not by looks.

Example 2. If ∠A = 120° and ∠H = 60°. Determine if the lines are parallel.

Solution:

Given ∠A = 120° and ∠H = 60°.

Since adjacent angles are supplementary, ∠A + ∠B = 180°

120 + ∠B = 180 → ∠B = 60°.

It is given that ∠H = 60°. We can see that ∠B and ∠H are exterior alternate angles.

When exterior alternate angles are equal, the lines are parallel.

Hence the lines p and q are parallel.

We can verify this using other angles.

If ∠H = 60°, ∠E = 120° since those two are on a straight line, they are supplementary.

Now, ∠A = ∠E = 120°. ∠A and ∠E are corresponding angles.

When corresponding angles are equal, the lines are parallel.

Likewise, we can prove using other angles too.

Example 3. If p and q are two lines parallel to each other and ∠E = 50°, find all the angles in the figure below.

Solution:

It is given ∠E = 50°.

The two lines are parallel

→ The corresponding angles are equal.

Since ∠E and ∠A are corresponding angles, ∠A = 50°.

→ The vertically opposite angles are equal.

Since ∠A and ∠C are vertically opposite to each other, ∠C = 50°.

Since ∠E and ∠G are vertically opposite to each other, ∠G = 50°.

→ The interior angles on the same side of the transversal are supplementary.

∠E + ∠D = 180° → 50 + ∠D = 180° → ∠D = 130°

→ ∠D and ∠B are vertically opposite angles. So ∠B = 130°.

→ ∠B and ∠F are corresponding angles. So ∠F = 130°.

→ ∠F and ∠H are vertically opposite angles. So ∠H = 130°.

∠D = ∠O + 90° → 130 = ∠O + 90 → ∠O = 40°

Also here is stuff I have been doing on a slide and by the way, it is GeoGebra stuff.