# 2-D Angles & Triangles

## What does it mean?

### Angle Definitions:

Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

Converse also true:
If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.

https://www.mathsisfun.com/geometry/alternate-exterior-angles.html

### Triangle Definitions:

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent.

If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally

If MBP is any triangle and LA is drawn parallel to MB, then PL/CE = PA/CE

## What does it look like?

A general example to help you recognize patterns and spot the information you're looking for

### Angles

Alternate Angles:
∠A = ∠H ∠G = ∠B

The angles inside a letter "Z" are alternate interior angles...

### Triangles

△ ADE and △ ABC are similar as they are equiangular. $$\frac{AD}{AB} = \frac{DE}{BC}$$ $$\frac{x + 4}{x} = \frac{6}{3}$$ $$\frac{x + 4}{x} = 2$$ $$x(\frac{x + 4}{x}) = x * 2$$ $$x + 4 = 2x$$ $$x + 4 - x = 2x - x$$ $$4 = x$$ $$x = 4$$

## You'll use it...

### Angles

Alternate exterior angles and same side interior angles are involved in the construction of buildings and bridges...

### Triangles

They are mostly used in engineering, architecture, and construction and can be used in scale drawings and finding distance height of the buildings.

## Video

### Acute, Right, and Obtuse Angles

Watch a Khan Academy Video »
Length: 5:33

## Video

### Congruent and Similar Triangles

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Length: 3:53

## Video

### Similar Triangles (part 2)

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Length: 9:55

## Video

### Similar Triangles

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Length: 9:34

## Video

### Equilateral and Isosceles Example Problems

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Length: 6:27

## Video

### Congruent Legs and Base Angles of Isosceles Triangles

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Length: 9:03

## Video

### The Pythagorean Theorem

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Length: 10:46

## Video

### Triangle Angle Example

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Length: 4:55

## Video

### Angles at the Intersection of Two Lines

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Length: 7:19

## Video

### Complementary and Supplementary Angles

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Length: 8:31

## Video

### The Angles for Congruent Triangles

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Length: 4:35