Chapter 18 - Geometry

What is the difference between lines, rays, and line segments?

• line: extends infinitely in both directions

• ray: a line that only extends from 1 of its points

• line segment: line that ends at both directions

How do you name lines, rays, and line segments?

** for rays, you can only name them in one direction. the endpoint is the first letter. it must be AB

lines and line segments can go either way AB or BA

acute angle

angle less than 90 degrees

obtuse angle

greater than 90 degrees, but less than 180 degrees

What do the interior angles of a triangle add up to?

180 degrees

Equal sides of a triangle means…

the angles are equal

The longest side of the triangle is located…

across from the biggest angle

Given any polygon, what happens when you take one exterior angle at each vertex?

The sum of the measures of exterior angles will always equal 360

720 degrees

these angles are not exterior angles which is why they don’t sum to 360 degrees

An exterior angle of a triangle is equal to….

the sum of its 2 remote interior angles

The 2 quantities are equal

An exterior angle of a triangle is equal to the sum of its 2 remote interior angles

What’s the area of a triangle?

(½ )(base)(height)

height is always perpendicular to the base of the triangle

What do you know about sums/difference of the lengths of the sides of triangles?

1. In any triangle, the sum of the lengths of any two sides of the triangle is greater than the length of the third side

2. In any triangle, the difference of the lengths of any two sides of the triangle is less than the length of the third side

How do you find the hypotenuse of a right triangle?

Use the Pythagorean theorem

Let c be the hypotenuse
c² = a² + b²

Given any triangle with sides a, b, and c, if c² = a² + b², then what must you know about the sides of the triangle?

the side opposite side C must measure 90 degrees and thus the triangle must measure 90 degrees

What are 2 Pythagorean triples?

1. 3-4-5

   • 3² + 4^{2 =} 5²

   • look for other ratios of this: {6, 8, 10}, {9, 12, 15}

2. 5-12-13

   • 5² + 12^{2 =} 13²

   • look for other ratios of this: {10, 24, 26}, {15, 36, 39}

if you see any of these side lengths of a triangle, you know the other dimensions

What is the formula to find the area of an isosceles triangle?

l²/2 = (leg₁)(leg₂)/2

let l be the length of one of the equal sides

What are the angles in an isosceles triangle?

90-45-45

2 even shorter sides, 1 long side