1 - Quia



|Acute angle |Geo |Angle with measure less than [pic] | |

| |Adjacent angles |Geo | |

| | | |Angles with a common vertex, common side and no interior |

| | | |points in common |

| |Angle |Geo |Union of two rays with common end point that are non-collinear|

| |Bisect |Geo |To cut in two equal parts |

| |Complementary angles |Geo |Two angles with a sum of 90 degrees |

| |Congruent |Geo |Two figures with equal measure |

| |Line |Geo |A series of points that extend in opposite directions without |

| | | |end |

| |Midpoint |Geo |Point that divides a segment into two equal parts |

| |Obtuse angle |Geo |Angle with measure greater than [pic] |

| |Parallel lines |Geo |Lines in the same plane that don’t intersect |

| |Perpendicular lines |Geo |Two lines that intersect to form right angles |

| |Plane |Geo | |

| | | |A flat surface with no thickness that extends indefinitely in |

| | | |all directions |

| |Point |Geo |A position in space with no size |

| |Ray |Geo |A part of a line that is bounded by one endpoint |

| |Right angle |Geo |Angle with measure of [pic] |

| |Segment |Geo |A part of a line that is bounded by two endpoints |

| |Skew Lines |Geo |Non-coplanar lines that do not intersect |

| |Supplementary angles |Geo |Two angles with a sum of 180 degrees |

| |Vertex |Geo |The common endpoint of two rays or segments |

| |Vertical angles |Geo |Two non-adjacent angles formed when two lines intersect |

| |Acute triangle |Geo |Triangle with all acute angles |

| |Altitude |Geo | |

| | | |Any line segment from a vertex perpendicular to the base, also|

| | | |the |

| | | |height of a figure |

| |Equilateral triangle |Geo |Triangle with all sides equal |

| |Isosceles triangle |Geo |Triangle with at least two equal sides |

| |Median (triangle) |Geo | |

| | | |In a triangle, the segment that joins a vertex and the |

| | | |midpoint of the opposite side |

| |Obtuse triangle |Geo |Triangle with one obtuse angle |

| |Right triangle |Geo |Triangle with a right angle |

| |Scalene triangle |Geo |Triangle with no equal sides |

| |Similar |Geo | |

| | | |Figures with corresponding angles congruent and corresponding |

| | | |sides in equal ratios |

| |Diagonal |Geo |A segment that connects nonconsecutive vertices of a polygon |

| |Hexagon |Geo |Six sided polygon |

| |Parallelogram |Geo |Polygon with opposite sides that are parallel |

| |Pentagon |Geo |Polygon with 5 sides |

| |Polygon |Geo |Plane figure with segments for sides |

| |Quadrilateral |Geo |Four sided polygon |

| |Regular Polygon |Geo |A polygon with all sides and angles congruent |

| |Rhombus |Geo |Quadrilateral with 4 equal sides |

| |Trapezoid |Geo |Quadrilateral with one pair of parallel sides |

| |Cone |Geo | |

| | | |3 -D figure with a circular base and a vertex not in the same |

| | | |plane as the base |

| |Cylinder |Geo | |

| | | |Three dimension figure with two circles as bases that are in |

| | | |parallel planes |

| |Net |Geo |2D drawing of a 3D solid |

| |Prism |Geo | |

| | | |Three dimension figure with polygonal bases in parallel planes|

| | | | |

| | | |with the other surfaces as parallelograms |

| |Pyramid |Geo | |

| | | |Three dimension figure with polygonal base and a vertex |

| | | |not in the plane of the base |

| |Slant Height |Geo |The altitude of a lateral face of a pyramid |

| |Sphere |Geo | |

| | | |Set of points in space a given distance from a given point |

| | | |called the center |

| |Surface Area |Geo |The sum of the area of all faces of a figure |

| |Volume |Geo |The number of cubic units it takes to fill a region |

| |Arc |Geo |Two points on a circle and all the points on the circle |

| | | |between them |

| |Central angle |Geo |Angle with its vertex at the center of a circle. |

| |Chord |Geo |A segment with its endpoints on a circle |

| |Circle |Geo |Set of points a given distance from a given point called the |

| | | |center |

| |Inscribed angle |Geo |An angle with its vertex on the circle and its sides are |

| | | |chords |

| |Secant |Geo |A line that intersects a circle at exactly two points |

| |Tangent |Geo |A line that intersects a circle at exactly one point |

| |Alternate exterior angles |Geo | |

| | | |Angles on opposite sides of transversal; on exterior of lines;|

| | | |nonadjacent |

| |Alternate interior angles |Geo | |

| | | |Angles on opposite sides of transversal; on interior of lines;|

| | | |nonadjacent |

| |Consecutive Exterior Angles |Geo | |

| | | |Angles that are on the same side of a transversal on the |

| | | |exterior of the parallel/intersected lines |

| |Consecutive Interior Angles |Geo | |

| | | |Angles that are on the same side of a transversal on the |

| | | |interior of the parallel/intersected lines |

| |Corresponding Angles |Geo | |

| | | |Angles on the same side of the transversal; one on the |

| | | |interior; one on the exterior; non-adjacent |

| |Transversal |Geo |A line or segment that intersects two different lines at |

| | | |different points |

| |Dilation |Geo |A transformation that alters the size of a figure, but not its|

| | | |shape |

| |Reflection |Geo |A transformation that flips all parts of a figure over a line |

| |Rotation |Geo | |

| | | |A transformation that flips all parts of a figure over two |

| | | |intersecting lines |

| |Transformation |Geo |The moving of all parts of a figure to a new location |

| |Translation |Geo | |

| | | |A transformation that slides all parts of a figure the same |

| | | |distance in the same direction |

| |Edge |Geo |The straight or curved paths connecting the nodes |

| |Network |Geo |A combination of nodes connected by edges |

| |Node |Geo |The points/vertices of a network |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

L to J Concepts

Geometry

Learning Essential Example Problem with Solution

1. Use proper notation to name angles, lines, [pic]

segments and rays.

[pic]

[pic]

[pic]

2. Find measures using bisectors [pic]

[pic]

find [pic]

3. Use a protractor to draw an angle [pic]

4. Measure the line segment to the nearest [pic] [pic]

sixteenth of an inch

5. Identify Parallel and Perpendicular Lines

6. Identify Adjacent, Vertical, Complementary Adjacent:

and Supplementary Angles

Vertical:

Complimentary:

Supplementary:

7. Pythagorean Theorem

[pic]

[pic]

8. 45º - 45º - 90º Special

Right Triangle Theorems

9. 30º – 60º – 90º Special [pic]

Right Triangle Theorems

[pic]

10. Find missing side of similar polygons

[pic] [pic]

11. Triangle Side Inequalities Name the longest side: [pic]

Find the range of the possible values of x.

8 < x < 18

12. Find the missing angle [pic]

[pic]

13. Find the value of an exterior angle x = 100

or a remote interior angle

14. Identify medians, altitudes, angle bisectors median: AE

and perpendicular bisectors of a triangle. angle bisector: AD

perpendicular bisector: EG

altitude: FB

15. Name all quadrilaterals that fit a given property Diagonals bisect each other:

Square, Rhombus,

Rectangle, Parallelogram

Diagonals are perpendicular:

Rhombus, Square

One pair of opposite sides parallel:

Trapezoid

16. Find the missing angles

17. Find the measure of an interior and Octagon Interior: 135

exterior angle of a regular polygon Exterior: 45

18. Find the interior and exterior angle 9 sides Interior: 1260

sum of a polygon( Interior sum =180(n-2) ) 180(9-2)=1260 Exterior: 360

19. Find the perimeter and area of a polygon Perimeter: 41 cm

Area: 56 cm2

20. Find the surface area and volume SA= Surface Area

of a 3D Solid V = Volume

21. Find the slant height 12 cm

22. Draw or identify the net/solid given the other Cube

23. Find measure of an arc measure of central angle = measure of the arc

24. Find the length of an arc Length of arc s = [pic]

25. Find the length of a chord AB = 8

26. Find the measure of central

and inscribed angles Inscribed = 40o

Central = 80o

27. Find the exact circumference and area Radius 8 in. Circumference =

Area = [pic]

28. List 5 ways to prove triangles congruent Defn, SSS, SAS, AAS, ASA

29. Identify a Transversal Line line s

30. Name the special angles formed given:

by the transversal line

Corresponding: 2 & 6, 3 & 8

1 & 5, 4 & 7

Alternate Exterior:2 & 7,1 & 8

Alternate Interior: 3 & 5,4 & 6

Consecutive Interior: 4 & 5

3 & 6

Consecutive Exterior: 1 & 7

2 & 8

31. Determine whether lines are parallel

32. Midpoint of a segment [pic]

A(2,-6) and B(8,-10)

[pic]

33. Distance between two points [pic]= 5

on a number line

[pic]

34. Distance between two points

on a coordinate plane A(2,4) and B(6,-8) [pic] = [pic]

[pic]

35. Slope of a line A(2,-7) and B(8,5) m = 2

m = [pic]

36. Point slope form of a line [pic]

37. Standard form of a line [pic]

A,B and C are integers and A[pic]0

38. Write the equation of a line given ( 2, 4 ) and ( 6, - 8) m = -3

two points.

y – 4 = -3( x – 2 )

39. Write the equation of a line given m = 8 point ( 3 , -5 )

one point and slope.

(y + 5) = 8(x– 3 )

40. Write the equation of a line y = [pic] so slope = 3/4

Parallel or perpendicular to a line Given point of ( -3, 2 )

Parallel equation is y – 2 = [pic]

Perpendicular equation is

41. Draw a network with 6 nodes and 10 edges

42. Find the Sine, Cosine and Tangent of an acute angle

43. Find missing sides and angles using Trig. Functions

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