Concepts 11

1
Concepts (1-1)

• Know
• Inductive Reasoning
• Conjecture
• Counterexample
• Do
• Use inductive reasoning to determine the next
  term(s) in a pattern
• Find a counterexample

2
Concepts (1-2)

• Know
• Point
• Space
• Line

• Collinear
• Plane
• Coplanar

• Do
• Recognize, name and draw (when appropriate) the
  above concepts
• Apply Postulates 1-1 through 1-4

3
Concepts (1-3)

• Know
• Segment
• Ray
• Opposite Rays

• Parallel Lines
• Skew Lines
• Parallel Planes

• Do
• Recognize, name and draw (when appropriate) the
  above concepts

4
Concepts (1-4)

• Know
• Congruent
• Midpoint
• Angle

• Midpoint
• Acute, obtuse, right, straight

• Do
• Determine the length and midpoint of a line
  segment
• Name an angle and determine the measure of an
  angle
• Apply the Segment Addition Postulate and solve
  for a variable
• Apply the Angle Addition Postulate and solve for
  a variable

5
Concepts (1-5)

• Know
• Perpendicular Lines
• Perpendicular Bisector
• Angle Bisector

• Do
• Recognize perpendicular lines, perpendicular
  bisectors, and angle bisectors
• Use perpendicular bisectors and angle bisectors
  to solve for a variable

6
Concepts (1-7)

• Know
• Perimeter of a polygon
• Area of a polygon

• Circumference of a circle
• Area of a circle

• Do
• Find the perimeter and area of a rectangle and
  irregular polygon
• Find the circumference and area of a circle

7
Concepts (2-1)

• Know
• Conditional Statement
• Hypothesis
• Conclusion

• Truth Value
• Converse

• Do
• Identify the hypothesis and conclusion of a
  conditional statement
• Write a statement as a conditional statement
• Write the converse of a conditional statement
• Determine the truth value of a statement

8
Concepts (2-2 and 5-4)

• Know
• Biconditional
• Inverse
• Contrapositive

• Do
• Write a conditional and its converse as a
  biconditional
• Write the inverse of a conditional statement
• Write the contrapositive of a conditional
  statement
• Determine the truth value of a statement

9
Concepts (2-3)

• Know
• Deductive Reasoning
• Law of Detachment
• Law of Syllogism

• Do
• Use the Law of Detachment to determine a
  conclusion
• Use the Law of Syllogism to determine a
  conclusion

10
Concepts (2-4)

• Know
• Properties of Equality
• Distributive Property
• Properties of Congruence

• Do
• Solve an algebraic equation for a variable and
  justify each statement using a 2-column format
• Classify a statement and determine whether it is
  a Property of Equality or Property of Congruence

11
Concepts (2-5)

• Know
• Vertical Angles
• Adjacent Angles
• Complementary Angles

• Supplementary Angles
• Proof and Theorem

• Do
• Identify the type of angle in a diagram and
  determine the measure of each angle
• Look at a diagram, solve for a variable and
  justify each statement using a 2-column format

12
Concepts (3-1)

• Know
• Transversal
• Alternate Interior Angles
• Same-Side Interior Angles

• Corresponding Angles

• Do
• Name and identify the above pairs of angles
• Given parallel lines cut by a transversal,
  determine the measure of each of the 8 angles
• Use parallel lines, a transversal, and the above
  pairs of angles to write an algebraic equation
  and solve for a variable
• Write a 2-column proof to determine that 2 angles
  are congruent or supplementary

13
Concepts (3-2)

• Know
• Parallel Lines
• Perpendicular Lines

• Do
• Determine whether 2 lines cut by a transversal
  are parallel
• Determine the value of a variable needed to
  guarantee that 2 lines cut by a transversal are
  parallel

14
Concepts (3-3)

• Know
• Triangle-Sum Theorem
• Equiangular, Acute, Obtuse, Right
• Equilateral, Isosceles, Scalene

• Interior and Exterior Angles
• Triangle Exterior Angle Theorem

• Do
• Find the missing angle measures in a triangle
• Classify a triangle by angles or by sides
• Use the Triangle Exterior Angle Theorem to
  determine missing interior or exterior angles

15
Concepts (3-4)

• Know
• Polygon
• Diagonal
• Convex and Concave
• Polygon Names

• Polygon Interior Angle-Sum Theorem
• Polygon Exterior Angle-Sum Theorem
• Regular Polygon

• Do
• Determine whether a figure is a polygon and, if
  so, whether it is convex or concave
• For a regular polygon, find the sum of the
  interior angles, the sum of the exterior angles,
  the measure of one interior angle, the measure of
  one exterior angle, and the number of total
  diagonals or the number of diagonals from one
  vertex

16
Concepts (3-5)

• Know
• Slope, y-intercept
• Slope-Intercept Form
• Standard Form

• Point-Slope Form
• Horizontal line
• Vertical line

• Do
• Given the Slope-Intercept Form of a line, find
  the slope and y-intercept and graph the line
• Given the Standard Form, graph the line
• Given a point and a slope, write the equation of
  the line in Point-Slope Form
• Given 2 points, write the equation of the line in
  Point-Slope Form
• Write the equations for and graph horizontal and
  vertical lines

17
Concepts (3-6)

• Know
• Slopes of Parallel Lines
• Slopes of Perpendicular Lines

• Do
• Given a graph or the equation of 2 lines,
  determine whether they are parallel,
  perpendicular, or neither
• Given the equation of one line, write the
  equation of a line that is either parallel or
  perpendicular to the given line
• Given horizontal or vertical lines, find the
  equations of parallel or perpendicular lines

18
Concepts (4-1)

• Know
• Congruent Figures
• Congruent Polygons
• Congruent Triangles

• Do
• Given two congruent polygons, name the
  corresponding congruent sides and angles
• Given two congruent polygons, find the measures
  of missing angles
• Determine if triangles are congruent (all sides
  and all angles are congruent)

19
Concepts (4-2)

• Know
• SSS
• SAS
• Included Sides and Angles

• Do
• Given a diagram, determine whether two triangles
  are congruent by SSS or SAS
• Write a 2-column proof to determine whether two
  triangles are congruent by SSS or SAS

20
Concepts (4-3)

• Know
• ASA
• AAS

• Do
• Given a diagram, determine whether two triangles
  are congruent by ASA or AAS
• Write a 2-column proof to determine whether two
  triangles are congruent by ASA or AAS

21
Concepts (4-4)

• Know
• AAA and SSA dont work
• CPCTC
• Perpendicular Bisector

• Do
• Describe why AAA and SSA dont work
• Use CPCTC to show that parts are congruent
• Write a 2-column proof to determine that parts
  are congruent by CPCTC
• Describe the effects of a perpendicular bisector

22
Concepts (4-5)

• Know
• Legs, Base, Vertex Angle, Base Angles of an
  Isosceles Triangle
• Isosceles Triangle Theorem and its Converse and
  Corollaries

• Do
• Given isosceles and equilateral triangles,
  determine the measures of missing sides and
  angles
• Use the bisector of the vertex angle of an
  isosceles triangle to find missing information
• Write a 2-column proof involving an isosceles or
  equilateral triangle

23
Concepts (4-6)

• Know
• Hypotenuse and Legs of a Right Triangle
• HL

• Do
• Write the 3 conditions for HL to work
• Given a diagram, determine whether two triangles
  are congruent by HL
• Write a 2-column proof to determine whether two
  triangles are congruent by HL

24
Concepts (4-7)

• Know
• Overlapping Congruent Triangles

• Do
• Find, separate and redraw overlapping congruent
  triangles
• Determine how the overlapping triangles are
  congruent
• Write a 2-column proof involving overlapping
  triangles

25
Concepts (Systems of Equations p. 209)

• Know
• System of Linear Equations
• Substitution

• Do
• Use substitution (or another method) to solve a
  system of linear equations

26
Concepts (5-1)

• Know
• Midsegment of a triangle
• Triangle-midsegment theorem
• Larger Side/Smaller Side

• Midpoint formula
• Distance formula

• Do
• Determine whether a segment in a triangle is a
  midsegment
• Find the measure of a midsegment or the third
  side
• Find pairs of parallel segments
• Graph a triangle, use the midpoint formula to
  find a midsegment, use the distance formula to
  determine the midsegment is 1/2 of the third
  side, and use the slope formula to show the
  midsegment and the third side are parallel

27
Concepts (5-2)

• Know
• Perpendicular-bisector theorem
• Distance from point to a line
• Angle-bisector theorem

• Do
• Use the perpendicular-bisector and angle-bisector
  theorems to find missing values in a triangle
• Graph a segment, graph its perpendicular
  bisector, and use the distance formula to verify
  a point on the perpendicular bisector is
  equidistant from the endpoints of the segment

28
Concepts (5-3)

• Know
• Concurrent Lines
• Point of Concurrency
• Circumcenter/circumscribed
• Incenter/inscribed

• Median/centroid
• Altitude/orthocenter

• Do
• In a triangle, draw a perpendicular bisector, an
  angle bisector, a median and an altitude
• Calculate the distance of the centroid to each
  vertex
• Match the point of concurrency with the part of
  the triangle and describe the result

29
Concepts (5-4)

• Know
• Negation
• Inverse
• Contrapositive
• Indirect Reasoning

• Do
• Write the inverse and contrapositive of a
  conditional
• Recognize the inverse and contrapositive in
  symbolic form
• Use indirect reasoning to draw a conclusion
• Write the first statement of an indirect proof
• Find statements that contradict each other

30
Concepts (5-5)

• Know
• Corollary to the Triangle Exterior Angle Theorem
• Larger Angle/Smaller Angle
• Larger Side/Smaller Side

• Do
• In a triangle, list angles or sides from largest
  to smallest or smallest to largest
• Given the measures of 3 segments, determine
  whether they could form a triangle
• Given the measures of 2 sides of a triangle,
  determine the range for the 3rd side

31
Concepts (6-1)

• Know
• Parallelogram, Rectangle, Rhombus, Square, Kite,
  Trapezoid, Isosceles Trapezoid

• Do
• Classify a quadrilateral according to definition
  and by appearance
• Graph a quadrilateral and determine its name
• Draw a hierarchy of quadrilaterals

32
Concepts (6-2)

• Know
• Properties of a parallelogram
• Consecutive angles
• Diagonals of a parallelogram

• Do
• Apply the properties of parallelograms to find
  the measures of missing sides and angles
• Given 3 or more parallel lines, determine which
  segments, if any, are congruent.

33
Concepts (6-3)

• Know
• Properties of a parallelogram

• Do
• Determine if a quadrilateral is a parallelogram
• Determine the values of variables that make a
  quadrilateral a parallelogram

34
Concepts (6-4)

• Know
• Properties of a rhombus
• Properties of a rectangle
• A square is both a rhombus and a rectangle

• Do
• Determine the measures of missing sides and
  angles in a rhombus and a rectangle
• Determine the lengths of diagonals in a rectangle

35
Concepts (6-5)

• Know
• Trapezoid legs, bases, base angles, isosceles
  trapezoid
• Properties of a trapezoid
• Properties of a kite
• Diagonals of a trapezoid and kite

• Do
• Find the measures of sides and angles in a
  trapezoid and a kite

36
Concepts (6-6)

• Know
• How to graph a quadrilateral on the coordinate
  plane

• Do
• Given a quadrilateral on the coordinate plane
  that has some coordinates containing variables
  instead of numbers, find the missing coordinates
• Given a quadrilateral on the coordinate plane
  that has some coordinates containing variables
  instead of numbers, prove the quadrilateral is a
  rectangle, square, rhombus or kite.

37
Concepts (7-1)

• Know
• Altitude (parallelogram and triangle)
• Area of a Rectangle
• Area of a Parallelogram
• Area of a Triangle

• Do
• Find the area of parallelograms and triangles
• Given the area of a parallelogram, find the
  height
• Graph a parallelogram or triangle and find its
  area

38
Concepts (7-Simplifying Radicals)

• Know
• Perfect squares (1 - 20)
• The rules for simplifying radicals

• Do
• Given a radical, find its simplified form
• Multiply and/or divide numbers involving
  radicals, and simplify the solution

39
Concepts (7-2)

• Know
• The Pythagorean Theorem and its converse
• Pythagorean Triples
• Family of Triples
• Right/Acute/Obtuse rules

• Do
• Use the Pythagorean Theorem to find a missing
  side of a triangle
• Use the Pythagorean Theorem to find a missing
  value and then determine the area of a triangle
• Use the sides of a triangle to determine whether
  it is right, acute or obtuse

40
Concepts (7-3)

• Know
• Isosceles Right Triangle
• 45-45-90 Triangle Theorem
• Parts of a 30-60-90 Triangle
• 30-60-90 Triangle Theorem

• Do
• Determine missing values in a 45-45-90
  triangle
• Determine missing values in a 30-60-90

41
Concepts (7-4)

• Know
• Area of a Trapezoid
• Area of a Rhombus
• Area of a Kite

• Do
• Determine the area of a trapezoid, rhombus, or
  kite
• Use the Pythagorean Theorem and special right
  triangles to find a missing value and then
  determine the area of a trapezoid, rhombus, or
  kite

42
Concepts (7-5)

• Know
• Radius and Apothem of a regular polygon
• Area of a Regular Polygon

• Do
• Determine the area of a regular polygon
• Use the Pythagorean Theorem and special right
  triangles to find a missing value and then
  determine the area of a regular polygon

43
Concepts (7-6)

• Know
• Parts of a circle central angle and arc
• Major arc, minor arc, semicircle

• Arc Addition Postulate
• Circumference
• Arc Length

• Do
• Determine the measures of the central angles and
  their related arcs in a circle
• Determine the measures of the central angles of a
  pie chart
• Find the circumference of a circle
• Find the arc length of an arc in a circle

44
Concepts (7-7)

• Know
• Area of a circle
• Sector of a circle
• Segment of a circle

• Area of a sector
• Area of a segment
• Arc Length

• Do
• Determine the area of a circle
• Determine the area of a sector of a circle
• Determine the area of a segment of a circle

45
Concepts (7-8)

• Know
• Probability of an event
• Probability of an area or region

• Do
• Determine the probability that an object would
  land in a certain part of a circle

46
Concepts (8-1)

• Know
• Properties of proportions

• Do
• Solve proportions
• Translate word problems into proportions and
  solve for a variable

47
Concepts (8-2)

• Know
• Definition of similar polygons
• Similarity statement
• Similarity ratio

• Do
• Determine if two figures are similar. If so,
  give the similarity statement and similarity
  ratio.
• Given two similar figures, find the values of
  missing variables.

48
Concepts (8-3)

• Know
• Angle-Angle Similarity
• Side-Angle-Side Similarity
• Side-Side-Side Similarity
• Indirect Measurement

• Do
• Determine if two triangles are similar. If so,
  give the similarity statement.
• Use indirect measurement and similar triangles to
  find a distance.

49
Concepts (8-4)

• Know
• Geometric mean
• Side-Angle-Side Similarity
• Side-Side-Side Similarity
• Indirect Measurement

• Do
• Determine the geometric mean of two numbers.
• Given a right triangle, recognize the three
  similar triangles created by the altitude.
• Determine missing values in the three similar
  triangles.

50
Concepts (8-5)

• Know
• Side Splitter Theorem
• Triangle-Angle Bisector Theorem

• Do
• Use the Side-Splitter Theorem to find missing
  values in a triangle.
• Use the Triangle-Angle Bisector Theorem to find
  missing values in a triangle.

51
Concepts (8-6)

• Know
• Similarity ratio
• Ratio of perimeters
• Ratio of areas

• Do
• For similar figures, find the similarity ratio,
  ratio of perimeters and ratio of areas.
• Given either the ratio or perimeters or ratio of
  areas, determine the other two ratios.

52
Concepts (9-1)

• Know
• Tangent Ratio (opposite over adjacent)

• Do
• Use the tan ratio to find a missing side or angle
  in a right triangle.

53
Concepts (9-2)

• Know
• Sine Ratio (opposite over hypotenuse)
• Cosine Ratio (adjacent over hypotenuse)
• SOH-CAH-TOA

• Do
• Use the sin ratio to find a missing side or angle
  in a right triangle.
• Use the cos ratio to find a missing side or angle
  in a right triangle.

54
Concepts (9-3)

• Know
• Angle of Elevation
• Angle of Depression

• Do
• Use the angle of elevation and/or angle of
  depression along with sin/cos/tan to find a
  missing side or angle in a right triangle (mainly
  word problems).

55
Concepts (9-5)

• Know
• Area of a regular polygon (A ½ ap)

• Do
• Use sin/cos/tan to find missing information
  needed to find the area of a regular polygon.

56
Concepts (9-9)

• Know
• Pythagorean Identity

• Do
• Show that, in a right triangle, (sin x)2 (cos
  x)2 1
• (where x is an angle)

57
Concepts (10-1/10.3)

• Prism
• Cylinder
• Base vs. Lateral Face
• Lateral Area
• Surface Area

• Know
• Polyhedron
• Face
• Edge
• Vertex
• Platonic Solid

• Do
• Determine the number of faces, edges, and
  vertices for a polyhedron
• Determine the lateral area and surface area for a
  prism
• Determine the lateral area and surface area for a
  cylinder

58
Concepts (10-4)

• Base
• Lateral Area
• Surface Area

• Know
• Pyramid
• Regular Pyramid
• Slant Height
• Cone
• Regular Cone

• Do
• Determine the lateral area and surface area for a
  pyramid
• Determine the lateral area and surface area for a
  cone

59
Concepts (10-5)

• Know
• Oblique
• Volume
• Composite Space Figure

• Do
• Determine the volume of a prism
• Determine the volume of a cylinder
• Determine the volume of a composite space figure

60
Concepts (10-6)

• Know
• Volume

• Do
• Determine the volume of a pyramid
• Determine the volume of a cone

61
Concepts (10-7)

• Know
• Sphere
• Center
• Radius
• Diameter
• Great Circle

• Do
• Determine the surface area of a sphere
• Determine the volume of a sphere
• Given the volume, find the surface area of a
  sphere

62
Concepts (10-8)

• Know
• Similar Solids
• Similarity Ratio
• Ratio of Surface Area
• Ratio of Volume

• Do
• Given the similarity ratio of two solids,
  determine the ratio of the areas and the ratio of
  the volumes
• Given the ratio of the volumes, determine the
  similarity ratio and the ratio of the areas

63
Concepts (11-1)

• Know
• Tangent to a circle
• Point of tangency
• Inscribed/circumscribed

• Do
• Use the fact that a radius and tangent are
  perpendicular to solve for missing information.
• Find the perimeter of a polygon circumscribed
  around a circle (using tangents)

64
Concepts (11-2)

• Know
• Chord
• Arc

• Do
• Use the relationship between congruent
  chords/arcs/central angles to find missing
  information.
• Use congruent chords equidistant from the center
  of a circle to find missing information.
• Use the fact that a diameter that is
  perpendicular to a chord bisects the chord and
  its arc.

65
Concepts (11-3)

• Know
• Inscribed angle (vertex is on the circle)
• Angle formed by a tangent and a chord

• Do
• Use the Inscribed Angles Theorem (and its
  corollaries) to find measures of arcs and angles
• Use the angle formed by a tangent and chord to
  find the measures of arcs and angles.

66
Concepts (11-4)

• Know
• Secant
• Angle formed by two lines that intersect inside
  the circle
• Angle formed by two lines that intersect
  outside the circle
• The product of the lengths of two segments

• Do
• Find the measures of angles and arcs formed by
  two lines that intersect inside a circle
• Find the measures of angles and arcs formed by
  two lines that intersect outside a circle
• Find the measures of segments that intersect
  inside or outside a circle

67
Concepts (11-5)

• Know
• Standard equation of a circle

• Do
• Graph a circle on the coordinate plane
• Given the graph of a circle, write the standard
  equation of the circle
• Find the center and radius from the standard
  equation
• Write the equation of a circle that passes
  through a certain point, given the center

68
Concepts (12-1)

• Know
• transformation
• reflection (flip)
• pre-image
• image

• isometry
• reflection in line r

• Do
• Name the corresponding angles and sides in an
  image
• Reflect a figure over line r

69
Concepts (12-2)

• Know
• translation (slide)
• vector

• Do
• Describe a translation in terms of a vector
• Describe a vector in words
• Translate an image using a vector

70
Concepts (12-3)

• Know
• rotation (turn)
• vector

• Do
• Rotate an image around a point using a protractor
• Determine the image of figure rotated around a
  point

71
Concepts (12-4)

• Know
• composition of transformations
• glide reflection

• Do
• Find an image using a composition of
  transformations
• Find an image using a glide reflection

72
Concepts (12-5)

• Know
• symmetry
• line symmetry
• reflections symmetry
• point symmetry

• Do
• Determine whether a shape has line symmetry,
  point symmetry, or both
• Draw all lines of symmetry
• Determine the angle of rotation

73
Concepts (12-6)

• Know
• tessellation
• tiling
• tessellation formula
• regular vs. semi-regular

• Do
• Determine whether a figure or figures tessellate
• Tessellate a figure

74
Concepts (12-7)

• Know
• dilation
• center
• scale factor
• enlargement vs. reduction

• Do
• Find the scale factor of a dilation
• Dilate an image centered at the origin with a
  given scale factor