Triangles

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There are various descriptions of triangles

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All Side Lengths and Angles are Equal:

... more on Equilateral Triangles

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Two Angles and Two Side Lengths are Equal

... more on Isosceles Triangles

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Nothing is equal

... more on Scalene Triangles

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Right Angled

To be right angled then the following must be true: Pythagorean theorem $$c^2=a^2+b^2$$ given $$c>a\ge b$$
... more on Right Angled Triangles

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Acute

To be acute then the following must be true: $$c^2<a^2+b^2$$ given $$c\ge a\ge b$$
... more on Acute Triangles

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Obtuse

To be obtuse then the following must be true: $$c^2>a^2+b^2$$ given $$c>a\ge b$$
... more on Obtuse Triangles

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Pythagorean Theorem

$$a^2+b^2=c^2$$

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Pythagoras Video 257:

Practice Questions;

Textbook Exercise.

Pythagoras on a graph Video:

Pythagoras: distance between points Video:

Practice Questions;

Textbook Exercise.

(See length of a line for more)

Pythagoras: 3D Video:

Practice Questions;

Textbook Exercise.

Pythagoras: rectangles/isosceles triangles Video:

Pythagoras: show triangle is right angle Video:

Practice Questions.

Pythagoras: area of a regular hexagon Video:

Practice Questions;

(Care of corbettmaths.com)

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A corollary of the Pythagorean theorem's converse is a simple means of determining whether a triangle is right-angled, obtuse, or acute, as follows. Let $c$ be the longest of the three sides and $a+b>c$ (to have a triangle according to the triangle inequality). Then the following apply:

• If $a^2+b^2=c^2$, then the triangle is right-angled;
• If $a^2+b^2>c^2$, then the triangle is acute;
• If $a^2+b^2<c^2$, then the triangle is obtuse.

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Proving the Pythagorean Theorem

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Perimeter

The perimeter of the triangle is givern by

$$P=a+b+c$$

Given that $c\ge a\ge b$ and $c\le a+b$

• where
• $P$ is the perimeter of the triangle,
• and
• $a$, $b$ and $c$ are the lengths of each side of the triangle.

Triangles: lengths of sides Video:

Practice Questions.

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Area of a Triangle

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Using Heron's Formula

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Questions

Area: triangle Video:

Practice Questions;

Textbook Exercise.

Trigonometry: area of a triangle Video:

Proof;

Practice Questions;

Textbook Exercise.

(Care of corbettmaths.com)

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