D I AG N O S T I C E R R O R A N A LY S I S

MEASUREMENT & GEOMETRY

44. CONGRUENCY

Congruency

• Two figures or objects are ___________ if they have the ______ shape size, or if one is the mirror image of the other.• If you place both

images on top of one another, GH and BC line up.

congruent same

45. SURFACE AREA

• How many sides of a cube are exposed as the surface area?• 26 (This includes the

bottom of model).• What is the surface

area of ONE side?• 3x3=9 sq. in.• 9x26=234 sq. in.

3

3

46. PYTHAGOREAN THEOREM

• What clues in the picture inform me that I must use the Pythagorean theorem?• a2+b2=c2

• 162+b2=202

• 256+b2=400• Solve for b.

a=

c=

b=?

47. CONVERSIONS

• Notice the initial units of measurements.

• Notice the conversions offered in the choices.

• You’ll have to convert the units into seconds or minutes.

• Divide the hour (60 minutes) into 6 kilometers.

• 60/6 = 10 minutes• 1 kilometer in 10 minutes.

48. SCALE MODELS AND PROPORTIONS

• Create the following proportion:

• Solve for x.

49. AREA OF TRIANGLE

• What is the formula for the area of a triangle?

• Correctly identify the base and height.

• Apply the formula.

base

height

This is NOT the height.

50. REFLECTION

• Reflection is the_________image across the ____ or _____- axis.• According to the question,

across which axis will the image cross?

• It will be across the y-axis.• POP QUIZ• What happens when

you translate a figure?

mirror

x

y

REFLECTION VS.

TRANSLATION

REFLECTION

• A figure can be reflected across the y-axis or across the x-axis.

• A problem will always direct you to “reflect across the ____ or ____ axis.”

TRANSLATION

• A figure can be translated up, down, left or right according to specific instructions.

• A problem will always direct you to translate with specific directions like the following:

• “ 2 units up”• “1 unit down and 3 units to

the right”• “1 unit down and 5 units to

the left”

x y

51. SCALE AND PROPORTION

• What is a key word in this problem?

• Volume is the key word.• How do you get the

volume of a cube?• Multiply the following:

(length)(width)(height)• We can give variables to

the cubes.• Small cube: (x)(x)(x)=

x3

• Large cube:(4x)(4x)(4x)=64x3

• Clearly, the larger cube is 64 times greater.

x

xx

4x

4x4x

52. PERIMETER

• You must know how to calculate the perimeter.

• The perimeter is the distance ___________ a figure.

• What are the measurements of all four sides?

• 25 + 12.5 + 25 + 12.5• Question: Why do two

sides measure 12.5?• Solve the problem.

around

53. PROPORTION

• Notice the time measurements.

• Create a proportion.

• Solve for x.• Is there another way you

can solve this problem?

54. CONVERSION WITH FORMULA

• Is this too easy?• To convert from Celsius to

Fahrenheit, plug in the known variable and solve for the unknown.

• Solve for F.

55. AREA OF CIRCLE

• How do we know that this question is asking for the area?

• Area is always measured in ___________ units.

• Question: How do I find the radius if they only give me the diameter?

• Label the parts of a circle.• Solve for the area of one

glass top.

square

56. PLOTTING FIGURES ON GRAPH

• It’s easy to plot the points.

• Now, you must know the definition of all four shapes.

: two bases, usually two parallel sides and two legs not parallel

:same opposite side, diagonals intersect.

:all four sides equal in length

:each opposite pair is parallel and the same length.