#### Park Links

Here are links to some of my favorite parks. The weblinks component provides an easy way to make links to external sites that are consistently formatted and categorised. You can create weblinks from the front end of your site.

https://astarmathsandphysics.com/component/weblinks/category/18-sample-data-weblinks/31-park-links.html?Itemid=829#### Proving Triangles are Congruent

To prove two triangles are congruent, it is sufficient two any of the following: The lengths of corresponding sides of each triangle are the same. If triangle 1 has lengths 4, 5 and 6 cm, and triangle 2 has lengths of 4, 5 and 6 cm, then the triangles...

https://astarmathsandphysics.com/gcse-maths-notes/637-proving-triangles-are-congruent.html#### Proving Triangles are Congruent

To prove two triangles are congruent, it is sufficient two any of the following: The lengths of corresponding sides of each triangle are the same. If triangle 1 has lengths 4, 5 and 6 cm, and triangle 2 has lengths of 4, 5 and 6 cm, then the triangles...

https://astarmathsandphysics.com/igcse-maths-notes/505-proving-triangles-are-congruent.html#### The Centre of Mass of a Scalene Triangle

Equilateral and isosceles triangles have symmetry, and this symmetry can be used to find the centre of the triangle. The centre of an equilateral triangle is quickly found to be two thirds of the distance from the vertex to the centre of the the...

https://astarmathsandphysics.com/ib-maths-notes/vectors-lines-and-planes/1174-the-centre-of-mass-of-a-scalene-triangle.html#### Proof of Formula for the Area of a Triangle

A triangle doesn't need to be right – angled for the area to be easily found. For the triangle – not rightangled, equliateral or isosceles - labelled as below, The area is calculated from To prove this formula, draw a line from B to meet the line AC...

https://astarmathsandphysics.com/gcse-maths-notes/626-proof-of-formula-for-the-area-of-a-triangle.html#### Similar Triangles Formed Between Parallel Lines

each other at a point A, angles on opposite sides of the point are the same. If parallel lines are drawn to construct two triangles, with one angle in each triangle the angle at A, then the triangles will be similar. In the diagram below, triangles ABC...

https://astarmathsandphysics.com/igcse-maths-notes/513-similar-triangles-formed-between-parallel-lines.html#### Formula for the Area of a Triangle

The area of a triangle is where is the base and is the perpendicular height. This formula is a bit artififical because we can take any side as the base and the height will be the perendicular distance of the opposite vertex from this chosen base. There...

https://astarmathsandphysics.com/ib-maths-notes/trigonometry/1124-formula-for-the-area-of-a-triangle.html#### Constructing an Equilateral Triangle or 60 Degree Angle

We can easily construct an equilateral triangle with a pair of compasses. Start by drawing a line AB. Open the compass to the same length as AB and put the compass needle at B. Draw an arc as shown. Now put the compass needle at A and draw another arc...

https://astarmathsandphysics.com/igcse-maths-notes/459-constructing-an-equilateral-triangle-or-60-degree-angle.html#### Constructing an Equilateral Triangle or 60 Degree Angle

We can easily construct an equilateral triangle with a pair of compasses. Start by drawing a line AB. Open the compass to the same length as AB and put the compass needle at B. Draw an arc as shown. Now put the compass needle at A and draw another arc...

https://astarmathsandphysics.com/gcse-maths-notes/573-constructing-an-equilateral-triangle-or-60-degree-angle.html#### Pascal's Triangle

Pascal's triangle provides a quick and easy way to calculate the coefficients of the binomial expansion, The entries in the table are calculated by adding the entties in each table immediately above to the left and right, with the exceptions of the...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1058-pascal-s-triangle.html#### Simple Trigonometry - Finding Angles in Right Angled Triangles

Simple trigonometry can be used with right angled triangles to find an angle given two sides, or a side given a side and one of the interior angles other than the right angle, With the sides of the triangle as labelled above, we can use one of the...

https://astarmathsandphysics.com/o-level-maths-notes/341-simple-trigonometry-finding-angles-in-right-angled-triangles.html#### Finding Sides of Right Angled Triangles

Simple trigonometry can be used with right angled triangles to a side given a side and one of the interior angles other than the right angle, With the sides of the triangle as labelled above, we can use one of the formulae: Example: If we have and and...

https://astarmathsandphysics.com/o-level-maths-notes/342-finding-sides-of-right-angled-triangles.html#### Constructing a Triangle With Three Given Sides

Suppose we want to construct a triangle with sides 5 cm, 6 cm and 7 cm. We use compass and ruler. Start with the base, and mark a line of 5 cm, PQ below. Open the compass to a length of 6 cm and draw an arc as shown below. Now open the compass to a...

https://astarmathsandphysics.com/igcse-maths-notes/461-constructing-a-triangle-with-given-sides.html#### Constructing a Triangle With Given Sides

Suppose we want to construct a triangle with sides 5 cm, 6 cm and 7 cm. We use compass and ruler. Start with the base, and mark a line of 5 cm, PQ below. Open the compass to a length of 6 cm and draw an arc as shown below. Now open the compass to a...

https://astarmathsandphysics.com/gcse-maths-notes/575-constructing-a-triangle-with-given-sides.html#### Trigonometry and Right Angled Triangles - Finding an Angle

There are three basic formulae, involving the ratio of the lengths of the sides. Given a right angled triangle, we first label the sides for the angle we choose or have been given: Given we have chosen the angle we label the sides for this angle....

https://astarmathsandphysics.com/gcse-maths-notes/681-trigonometry-and-right-angled-triangles-finding-an-angle.html#### Trigonometry - Right Angled Triangles - Finding a Side

There are three basic formulae, involving the ratio of the lengths of the sides. Given a right angled triangle, we first label the sides for the angle we have: If we have the angle shown, we label the sides for this angle. Opposite = is the side...

https://astarmathsandphysics.com/gcse-maths-notes/682-trigonometry-right-angled-triangles-finding-a-side.html#### Proof That a Triangle Drawn in a Semicircle is Right Angled

If a triangle is drawn in a semicircle, with the diameter forming one side of the circle, as below, the angle formed opposite the diameter (angle ) is a right angle. The proof follows straight from the fact that the angle subtended by an arc at the...

https://astarmathsandphysics.com/gcse-maths-notes/632-proof-that-a-triangle-drawn-in-a-semicircle-is-right-angled.html#### The Myth of the Bermuda Triangle

Many people have heard of the Bermuda triangle as an area of the Atlantic where ships disappear without trace. Various explanations have been put forward, among them alien abductions, space time vortices – whatever that means – and sea monsters....

https://astarmathsandphysics.com/gcse-physics-notes/863-the-myth-of-the-bermuda-triangle.html#### The Myth of the Bermuda Triangle 2

Many people have heard of the Bermuda triangle where planes or ships disappear without trace. Most famously in 1945, an entire flight of five US Navy TBM Avenger Torpedo bombers disappeared, together with the plane sent to search for them. There are...

https://astarmathsandphysics.com/gcse-physics-notes/864-the-myth-of-the-bermuda-triangle-2.html#### Proof of Backwards Form of Triangle Inequality

The backwards form of the trangle inequality states that for any two vectors and The meaning of the theorem is shown in the following diagram. We can also illustrate with real numbers, which may be considered one dimensional vectors. Take and The proof...

https://astarmathsandphysics.com/ib-maths-notes/proofs/1080-proof-of-backwards-form-of-triangle-inequality.html