Right Triangles and Pythagorean Theorem

Standard

The Pythagorean Theorem states that, in a right triangle, the two smaller squares made from the triangles legs add up to equal the biggest square made from the hypotenuse.

Pythagoras             

The lengths of the legs are commonly labeled as a and b and the hypotenuse length is labeled as c.

REMEMBER:

HYPOTENUSE: c is the longest side of the triangle

LEGS: a and b are the other two sides

What is the Pythagorean Theorem?

In short the Pythagorean Theorem can be explain with the formula below.

a2 + b2 = c2

AGAIN, THIS IS ONLY TRUE FOR RIGHT TRIANGLES!

Here are other examples:

When not knowing the Pythagorean Theorem can cost you $15,000.

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Angle and Triangle Relationships

Standard

Degrees

A degree is a unit of measurement used to measure angles.

We can measure all Angles in Degrees.

There are 360 degrees in one Full Rotation (one
complete circle around

The Degree Symbol: °

We use a little circle ° following the number to mean degrees.

For example 90° means 90 degrees

Angles

types of angle

In One Diagram

This diagram might make it easier to remember:

Also: Acute, Obtuse and Reflex are in alphabetical order.

Supplementary Angles

Two Angles are Supplementary if they add up to 180 degrees.
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°.

Notice that together they make astraight angle.

But the angles don’t have to be together.

These two are supplementary because 60° + 120° = 180°

Complementary Angles

Two angles are Complementary when they
add up to 90 degrees
(a Right Angle right angle).

These two angles (40° and 50°) are
Complementary Angles, because they add up to 90°.Notice that together they make a right angle right angle.
But the angles don’t have to be together.

These two are complementary because 27° + 63° = 90°

Angle Relationships

Interior Angle

An Interior Angle is an angle inside a shape.

Exterior Angle

The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.

Angles On One Side of A Straight Line

Angles on one side of a straight line will always add to 180 degrees.

If a line is split into 2 and you know one angle you can always find the other one.


30° + 150° = 180°

Interior Angles of Polygons

An Interior Angle is an angle inside a shape.

Triangles

The Interior Angles of a Triangle add up to 180°

90° + 60° + 30° = 180°

80° + 70° + 30° = 180°

It works for this triangle!

Let’s tilt a line by 10° …

It still works, because one angle went up by 10°, but the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

90° + 90° + 90° + 90° = 360°

80° + 100° + 90° + 90° = 360°

A Square adds up to 360°

Let’s tilt a line by 10° … still adds up to 360°!

The Interior Angles of a Quadrilateral add up to 360°

Because there are Two Triangles in a Square

The interior angles in this triangle add up to 180°

(90°+45°+45°=180°)

… and for this square they add up to 360°

… because the square can be made from two triangles!