# Geometry

- StudyBlue
- Utah
- Brigham Young University
- Geometry

**Created:**2014-04-21

**Last Modified:**2014-04-23

_{1}-y

_{2}/x

_{1}-x

_{2}

- interior angles
- perimeters
- area

- surface area
- volume

b = base

h = vertical height

^{2}+ b

^{2}+ c

^{2 }= d

^{2}

**Of all quadrilaterals with a given perimeter, the ______ has the largest area**

**Of all quadrilaterals with a given area, the ______ has the minimum perimeter**

**the sum of any two sides of a triangle must be**

**GREATER THAN the third side**

**greater than**

- 3-4-5
- 5-12-13
- 8-15-17

- corresponding angles
- corresponding sides

^{2}: b

^{2}.

*The lengths being compared do not have to be sides--they can represent heights or perimeters. In fact, the figures do not even have to be triangles. The principle holds true for any similar figure or polygon.

^{2}

*V*= π

*r*

^{2}

*h*

*A*= 2(∏

*r*

^{2}) + 2∏

*r*

*h*

**if you are given two sides of a triangle or parallelogram, you can maximize the area by:**

- The angles formed by any intersecting lines
- The angles formed by parallel lines cut by a transversal

**supplementary angles**

**vertical angles**

- vertical line
- zero in denominator

- forms a 90 degree angle with the segment
- divides the segment exactly in half

- the products of the two slopes is -1
- the only exception occurs when one line horizontal and the other line is vertical, since vertical lines have undefined slopes

__both__lines

**discriminant**in the quadratic equation

- >0 = two roots, two x-intercepts
- =0 =1 root, one x-intercept
- <0 = no roots, the parabola never touches the x-axis, no x-intercepts

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