Qr(3)Plane Geometry

Front 1

midpoint

Back 1

halfway

if section length is known, can divide by 2 to get the length from one end to the midpoint

Front 2

sum of interior angles of a triangle

Back 2

180 degrees

Front 3

measure of an exterior angle of a triangle

Back 3

the sum of the measures of the remote interior angles of the triangle

Front 4

sum of exterior angles of any triangle

Back 4

360 degrees

Front 5

area of a triangle

Back 5

1/2(base)(height)

Front 6

triangle inequality theorem

Back 6

Each side of a triangle is greater than the difference and less than the sum of the other two sides.

Ex, if given the length one side is 3 and another is 7, then the length of the third side must be greater than 7-3=4 and less than 7+3=10.

Front 7

similar triangles

Back 7

triangles that have the same shape: corresponding angles are equal, corresponding sides are proportional

Front 8

isosceles triangles

Back 8

a triangle that has two equal sides, angles opposite the equal sides are equal

Front 9

equilateral triangle

Back 9

a triangle that has three equal sides. All angles are also equal, all 60 degrees.

Area of an equilateral triangle = (s^2 x sqrt[3])/4

Front 10

right triangle

Back 10

a triangle with a 90 degree angle. Sides that form the right angle are called legs.

Area of a right triangle = 1/2(leg 1)(leg2)

Front 11

Pythagorean theorem

Back 11

for right triangles -it allows you to find the third side if given other two sides.

(leg1)^2 + (leg2)^2 = (hypotenuse)^2

Front 12

Pythagorean triplet

Back 12

a set of integers that fits the Pythagorean theorem

3:4:5

Front 13

3-4-5 triangle

Back 13

if a right triangle's leg ratio is 3:4, or if the leg-hypotenuse ratio is 3:5 or 4:5, then it is a 3-4-5 triangle, so the Pythagorean theorem is not needed to find the missing side.

Ex: if one leg is 30 and the hypotenuse is 50. This is a 10 times 3-4-5. The other leg is 40.

Front 14

5-12-13 triangles

Back 14

another Pythagorean triplet right triangle. Just figure out what multiple of 5-12-13 it is to find the missing side.

Ex: if the base leg is 36 and hypotenuse is 39. This is 3 times 5-12-13. The other leg is 3x5=15.

Front 15

45 degree-45 degree-90 degree triangle

Back 15

side of this right triangle are in a ratio of 1:1:sqrt(2)

Ex: if one leg is 3, then the other leg is also 3, and the hypotenuse is equal to a leg times sqr(2), or 3sqr(2)

Front 16

30-60-90 degree triangles

Back 16

right triangle whose sides are in a ratio of 1:sqrt(3):2

Ex. if the hypo is 6, then the shorter leg is half that, or 3; and then the loner is equal to teh short leg times sqr(3), or 3sqr(3).

Front 17

hidden special triangles

Back 17

sometimes adding a line segment to a shape can create special triangles for you to use to solve the problem

dropping altitudes and perpendiculars are often very useful

Front 18

special quadrilaterals

Back 18

trapezoids, parallelograms, rectangles, rhombus, square

Front 19

trapezoid

Back 19

4 sided figure with one pair of parallel sides and one pair of non parallel sides

area= [(base1+base2)/2]x height
*Think of formula as avg of bases (the two parallel sides) times the height (length of the perpendicular altitude)

Front 20

Define parallelograms and how do you determine its area?

Back 20

4-sided figure, two pairs of parallel sides. Opposite sides are equal, opposite angles are equal. Consecutive angles add up to 180'.

area= base x height

Note: You can use a side for the height only when the side is perpendicular to the base, in which case you have a rectangle.

Front 21

rectangle

Back 21

4-sided figure with 4 right angles
opposite sides are equal
perimeter is equal to the sum of the 4 sides
area=length x width

Front 22

rhombus

Back 22

4-sided figure with 4 equal sides. Another form of a parallelogram.

area=base x height

Front 23

square

Back 23

4 sided figure with four right angles and four equal sides. Another form of rectangle, parallelogram, and a rhombus.

area=(side)^2

Front 24

hexagon

Back 24

6 equal sides

area = [3s^2sqrt(3)]/2

Front 25

circumference

Back 25

perimeter of a circle or measurement of length.

2(pi)r or (pi)d.... in terms of diameter.

Front 26

length of an arc

Back 26

piece of a circumference

Length of arc = (n/360)(2 pi r)
n=degree of arc's central angle

Ex. if r=5,central angle=72' then arc length is (72/360)2pi(5)=2pi.

Front 27

area of a circle

Back 27

pi r^2

Front 28

area of a sector

Back 28

sector - piece of the area of a circle

(n/360)(pi r^2)

Front 29

In a Nutshell: Basic Traits of Triangles

Back 29

1. interior angles add up to 180'.
2. Ext angle=sum of remote int angles.
3. Ext angles add up to 360'.
4. Area of a triangle=1/2(B)(H)
5. Each side is greater than the difference of the other two sides.

Front 30

Test makers like to write probems that combine the concepts of perimeter and area. What should you remember?

Back 30

perimeter and area are not directly related.

Front 31

What is the best way to approach a FIGURELESS geometry problem?

Back 31

Sketch a figure on your own.

Front 32

What are the four things you have to know how to find in a circle?

Back 32

1. circumference
2. length of an arc
3. area
4. area of a sector

Front 33

What is half of 5/12?

Back 33

5/24

Front 34

If the ratio of AB to BC is 7 to 5, what does that mean?

Back 34

7 and 5 are proportions not lengths. you write it as AB=7/12 and BC=5/12.

Front 35

In a parallelogram (PQRS), is the PQ side equal to the height?

Back 35

No.

Front 36

If given a shape within the circumference of a cirlce, what are the steps to solve the problem?

Back 36

1. draw a radius: all the radii of a circle are equal, so within each of the two triangles, the angles opposite the radii are equal