Geometry

Question 1

Bisecting line

Answer 1

Splits something into 2 EQUAL parts`

Question 2

Be aware that polygons do not have to…

Answer 2

…be “regular.”

Regular = all sides the same lengt

Question 3

Sum of interior angles of a triangle

Answer 3

Add up to 180

Question 4

Sum of interior angles of a quadrilateral (4 sides)

Answer 4

Add up to 360

Question 5

The sum of the interior angles of every pentagon (5 sides)

Answer 5

Add up to 540

Question 6

Hexagon - sum of interior angles…

Answer 6

…add up to 720

Question 7

Sum of interior angles of any polygon =

Answer 7

(n-2)180

Question 8

Sum of exterior angle and interior angle…

Answer 8

…always equals 180

Question 9

Num of interior angles and exterior angles in every polygon

Answer 9

Is equal (triangle has 3 interior angles, that add up to 180, and 3 exterior angles)

Question 10

The sum of the exterior angles of ANY polygon…

Answer 10

…is always equal to 360

Question 11

For triangles - an EXTERIOR angle of a triangle is always equal to….

Answer 11

…the SUM Of the NON-ADJACENT interior angles.

Question 12

Never assume…

Answer 12

…that the lines are parallel, angle is right, shape is a square, etc. (Unless the exam explicitly states otherwise)

Question 13

Tricky problem with lines and angles…

Answer 13

1. Draw the diagram
2. Look for relationships you know
3. Don’t be afraid to “tune out” lines temporarily
4. If you can find >1 equation , COMBINE equations using subtraction or elimination
5. Look back at the diagram to see if your solutions make sense with the general shape

Question 14

180-x trick

Answer 14

Label ALL of the interior (or exterior) angles of the polygon, using 180-x

Question 15

Isosceles

Answer 15

2 angles of = measure, 2 sides of = measure.

NOTE - an equilateral is just a SPECIAL type of isosceles.

Question 16

Pythagorean triples

Answer 16

3-4-5 (6-8-10; 9-12-15; 12-16-20; 15-20-25)
5-12-13 (10-24-26)
8-15-17
7-24-25

Question 17

45-45-90 triangles [isosceles right triangle]

Answer 17

x:x:x(sq.rt of 2)

Question 18

45-45-90 Short-Cut

Answer 18

CUT the hypothenuse in HALF and MULTIPLY the result by sq. root of 2

Question 19

Every equilateral triangle

Answer 19

Is composed of TWO 30-60-90 triangles

Question 20

Perimeter and triangle inequality theorem

Answer 20

Sum of any two sides of any triangle must be greater than the third side. Conversely, the difference of any two sides must be less than the third.

LESS THAN THE SUM, BUT GREATER THAN THE DIFFERENCE

Question 21

Parallelogram - adjacent angles

Answer 21

Always add up to 180

Question 22

Diagonals of a parallelogram…

Answer 22

…bisect one another and split the shape into two equilateral triangles

Question 23

Area of a parallelogram

Answer 23

Is equal to BASE times HEIGHT

Question 24

Area of a trapezoid

Answer 24

Average of bases x height

Question 25

Units in a surface area question…

Answer 25

…should be squared

Question 26

Volume of a rectangular solid

Answer 26

Length x Width x Height

Question 27

Units when calculating volumen…

Answer 27

Should be cubed

Question 28

How to determine the interior diagonal of a rectangular slid?

Answer 28

The Diagonal of a Rectangular Solid = square root of (lˆ2 + wˆ2 + hˆ2)

Question 29

Diagonal of a Cube

Answer 29

Diagonal of a Cube = s (square root of 3)

S = side length

Question 30

To find the midpoint if you know the two coordinates

Answer 30

Average the x-coordinates and y-coordinates

Question 31

Perpendicular lines

Answer 31

The product of their slopes = -1

Question 32

Surface area of a rectangular solid = ?

Answer 32

2(lw + wh + lh)