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Geometry Proficiencies
1. Apply the midpoint
formula to solve
problems in a
coordinate plane.
I can…
Where can I find help?
I can find the midpoint of two
points on a number line (1-D).
http://www.khanacademy.org/math/algebra/linear-equationsand-inequalitie/v/midpoint-formula
I can find the midpoint to two
points on a coordinate plane
(2-D).
2. Identify, apply, and
analyze angle
relationships among
two or more lines and
a transversal to
determine if lines are
parallel, perpendicular,
or neither.
I can identify when angles
have the following relations:
vertical angles, linear pair,
alternate interior angles,
alternate exterior angles,
corresponding angles,
consecutive interior angles.
I can determine the measure
of all eight angles formed
when given parallel lines cut
by a transversal.
http://www.khanacademy.org/math/geometry/angles/v/anglesat-the-intersection-of-two-lines
http://www.khanacademy.org/math/geometry/angles/v/anglesformed-between-transversals-and-parallel-lines
http://www.khanacademy.org/math/geometry/angles/v/anglesof-parallel-lines-2
http://www.khanacademy.org/math/geometry/angles/v/angles-part-3
http://www.khanacademy.org/math/geometry/angles/v/theangle-game
3. Apply theorems,
properties, and
definitions to
determine, identify,
and justify congruency
or similarity of triangles
and classify
quadrilaterals.
I can justify congruence of
triangles using SSS, SAS,
ASA and AAS.
I can write congruence
statements of two congruent
shapes.
http://www.khanacademy.org/math/geometry/triangles/v/congr
uent-and-similar-triangles
http://www.khanacademy.org/math/geometry/triangles/v/congr
uent-triangles-and-sss
http://www.khanacademy.org/math/geometry/triangles/v/other
-triangle-congruence-postulates
http://www.khanacademy.org/math/geometry/angles/v/moreon-why-ssa-is-not-a-postulate
http://www.khanacademy.org/math/geometry/triangles/v/findin
g-congruent-triangles
http://www.khanacademy.org/math/geometry/triangles/v/congr
uent-triangle-proof-example
www.khanacademy.org/math/geometry/triangles/v/congruenttriangle-example-2
4. Apply theorems of
corresponding parts of
congruent and similar
figures to determine
missing sides and
angles of polygons.
I can determine side lengths
and angles measures based
on triangles being similar.
I can determine missing side
lengths and angle measures
based on triangles being
congruent.
http://www.khanacademy.org/math/geometry/triangles/v/simila
r-triangle-basics
http://www.khanacademy.org/math/geometry/triangles/v/simila
rity-postulates
http://www.khanacademy.org/math/geometry/triangles/v/simila
r-triangles
http://www.khanacademy.org/math/geometry/triangles/v/simila
r-triangles--part-2
http://www.khanacademy.org/math/geometry/triangles/v/simila
r-triangle-example-problems
http://www.khanacademy.org/math/geometry/triangles/v/simila
rity-example-problems
http://www.khanacademy.org/math/geometry/triangles/v/appli
cation-of-similar-triangles
5. Recognize and
identify line and
rotational symmetry of
two dimensional
figures. (To exceed
classify freeze groups)
I can identify lines of reflection http://www.mathsisfun.com/geometry/symmetry-reflection.html
of two dimensional shapes.
http://en.wikipedia.org/wiki/Rotational_symmetry
I can identify the angle of
rotational symmetry of two
http://www.mathsisfun.com/geometry/symmetrydimensional shapes.
rotational.html
(to exceed) I can classify
horizontal repeating patterns
as one of the 7 frieze groups.
http://mathdl.maa.org/images/upload_library/4/vol1/architectur
e/Math/seven.html
http://euler.slu.edu/escher/index.php/Frieze_Patterns#The_Se
ven_Frieze_Groups
6. Identify and
perform single and
multiple
transformations of
geometric figures in a
plane, including
translations, origincentered dilations,
reflections across
either axis or y = + - x,
and rotations about the
origin in multiples of 90
degrees.
I can perform single
transformations on shapes
composed of ordered pairs.
http://www.mathsisfun.com/geometry/transformations.html
I can perform multiple
transformations on shapes
composed of ordered pairs.
http://www.mathsisfun.com/geometry/reflection.html
http://www.mathsisfun.com/geometry/rotation.html
http://www.mathsisfun.com/geometry/translation.html
I can identify the type of
http://www.mathsisfun.com/activity/shapes-symmetry.html
transformation performed on a
shape. (reflection, rotation,
translation/slide, and glide
see handouts
reflection)
7. Express square
roots in equivalent
radical form and their
decimal
approximations when
appropriate. Also
explore higher order
roots.
I can simplify square roots
(camp gitagoomee).
http://www.khanacademy.org/math/algebra/exponentsradicals/v/understanding-square-roots
I can use a calculator to get a
decimal approximation of a
square root.
http://www.khanacademy.org/math/algebra/exponentsradicals/v/approximating-square-roots
I can simplify higher order
roots like cube roots.
I can rationalize the
denominator. (I can get the
radical out of the
denominator.)
http://www.khanacademy.org/math/algebra/exponentsradicals/v/square-roots-and-real-numbers
http://www.khanacademy.org/math/algebra/exponentsradicals/v/simplifying-square-roots
http://www.khanacademy.org/math/algebra/polynomials/v/r
ationalizing-denominators-of-expressions
8. Use the
Pythagorean Theorem
to solve for unknown
lengths in right
triangles and the
distance formula.
(Determine the
missing dimensions of
Special Right
Triangles)
I can find the length of a side
(leg) of a right triangle when
given another side (leg) and
the hypotenuse.
I can find the length of the
hypotenuse of a right triangle
when given the two other
sides (legs).
I can use the distance formula
to find the distance between
two sets of ordered pairs.
I can use the 45-45-90 and
30-60-90 special right
triangles to find the lengths of
unknown sides of similar
triangles.
http://www.khanacademy.org/math/geometry/triangles/v/introd
uction-to-the-pythagorean-theorem
http://www.khanacademy.org/math/geometry/triangles/v/thepythagorean-theorem
http://www.khanacademy.org/math/geometry/triangles/v/pytha
gorean-theorem-ii
http://www.khanacademy.org/math/algebra/linear-equationsand-inequalitie/v/distance-formula
http://www.khanacademy.org/math/geometry/triangles/v/4545-90-triangles
http://www.khanacademy.org/math/geometry/triangles/v/4545-90-triangle-side-ratios
http://www.khanacademy.org/math/geometry/triangles/v/introto-30-60-90-triangles
http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangles-ii
http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangle-side-ratios-proof
http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangle-example-problem
9. Use Trig ratios to
solve for unknown
lengths in right
triangles.
I can use trigonometric ratios
to determine unknown lengths
of the sides of right triangles.
(when given one angle and
one side)
http://www.khanacademy.org/math/trigonometry/v/basictrigonometry
I can use trigonometric ratios
to determine unknown angles
of a right triangle. (when
given two sides)
http://www.khanacademy.org/math/trigonometry/v/using-trigfunctions
http://www.khanacademy.org/math/trigonometry/v/basictrigonometry-ii
http://www.khanacademy.org/math/trigonometry/v/using-trigfunctions-part-ii
http://www.khanacademy.org/math/trigonometry/v/trigonometr
y-word-problems--part-1
http://www.khanacademy.org/math/trigonometry/v/trigonometr
y-word-problems--part-2
http://www.khanacademy.org/math/trigonometry/e/law_of_cos
ines
http://www.khanacademy.org/math/trigonometry/v/law-ofcosines
10. Determine if three
given lengths form a
triangle. If the given
lengths form a triangle,
classify it as acute,
right, or obtuse.
I can determine if three given
lengths can make a triangle.
http://www.geom.uiuc.edu/~wanous/definitionofatriangle.html
http://www.apluspublishing.com/aplus4.html
I can determine if a triangle is
a right, obtuse or acute
triangle.
I can determine if a right
triangle is a special right
triangle.
http://www.wikihow.com/Determine-if-Three-Side-LengthsAre-a-Triangle
http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri30.
htm
http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri45.
htm
11. Determine the
missing dimensions,
angles, or area of
quadrilaterals,
triangles, circles,
composite shapes,
and shaded regions.
I can determine the area of
quadrilaterals, triangles,
circles, composite shapes and
shaded regions.
http://www.khanacademy.org/math/geometry/basic-geometry/v/perimeterand-area-basics
I can determine missing
dimensions of the above
shapes when given the area
and some of the dimensions.
http://www.khanacademy.org/math/geometry/basic-geometry/v/perimeterand-area-of-a-non-standard-polygon
http://www.khanacademy.org/math/geometry/basic-geometry/v/area-andperimeter
http://www.khanacademy.org/math/geometry/polygons-quadsparallelograms/v/quadrilateral-overview
http://www.khanacademy.org/math/geometry/circles-topic/v/circles--radius-diameter-and-circumference
http://www.khanacademy.org/math/geometry/circles-topic/v/area-of-acircle
http://www.khanacademy.org/math/geometry/triangles/v/triang
le-area-proofs
12. Identify, classify,
model, sketch, and
label representations
of three-dimensional
objects from nets and
from different
perspectives.
I can identify and classify
three dimensional shapes
from nets.
http://www.primaryresources.co.uk/maths/mathsE3.htm#3
http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/
3d/index.htm
I can sketch a net of any three
dimensional shape.
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=we
b&cd=4&ved=0CDMQFjAD&url=http%3A%2F%2Fcollege.cen
gage.com%2Fmathematics%2Fbassarear%2Felementary_sc
hool%2F3e%2Fstudents%2Fsample%2Fch08_03.pdf&ei=jKIUP3aAo6UjAKX4YCgAg&usg=AFQjCNHOS0XO4MCgzWMh
knlXMTILgz0_Wg
13. Identify and apply
formulas for surface
area and volume of
spheres, right solids,
including rectangular
prisms and pyramids;
cones; and cylinders;
and compositions
thereof. Solve related
context-based
problems.
I can determine the surface
area of rectangular prisms
and pyramids; cones; and
cylinders and compositions
thereof.
I can determine the volume of
rectangular prisms and
pyramids; cones; and
cylinders and compositions
thereof.
http://www.khanacademy.org/math/geometry/basic-geometry/v/solidgeometry-volume
http://www.khanacademy.org/math/geometry/basic-geometry/v/cylindervolume-and-surface-area
http://www.khanacademy.org/math/geometry/basic-geometry/v/volume-ofa-sphere
14. Identify and apply
formulas to solve for
the missing
dimensions of spheres
and right solids,
including rectangular
prisms and pyramids,
cones, and cylinders,
both numerically and
symbolically.
I can determine unknown
dimensions of rectangular
prisms and pyramids; cones;
and cylinders and
compositions thereof when
given the surface area or
volume.
http://www.khanacademy.org/math/geometry/basic-geometry/v/solidgeometry-volume
http://www.khanacademy.org/math/geometry/basic-geometry/v/cylindervolume-and-surface-area
http://www.khanacademy.org/math/geometry/basic-geometry/v/volume-ofa-sphere
15. Apply a scale
factor to determine
similar two- and threedimensional figures,
are similar. Compare
and compute their
respective areas and
volume of similar
figures.
I can determine the scale
factor, ratio of areas and ratio
of volumes when given one of
the fore mentioned.
I can use the scale factor to
an unknown dimension of two
similar objects.
I can use the ratio of areas to
find the unknown area of one
of two similar objects.
I can use the ratio of volumes
to find the unknown volume of
one of two similar objects.
http://www.khanacademy.org/math/algebra/ck12-algebra1/v/scale-and-indirect-measurement
Bonus #1. In
problems involving
circles, apply theorems
and properties of
chords, tangents, and
angles; and theorems
and formulas of arcs
and sectors.
I can find lengths of chords,
arcs and tangent lines when
given enough information.
(enough being all but one part
of theorems of circles).
I can find angles formed by
chords, arcs and tangent lines
when given enough
information.
http://www.khanacademy.org/test-prep/california-standardstest/geometry-2/v/ca-geometry--circle-area-chords-tangent