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Edited 6/25/12
Beaverton School District
Geometry Long-term and Supporting Learning Targets
MA.HS.GE.ALT.01: I can demonstrate my understanding of the foundations of
geometry.
MA.HS.GE.AST.01.1: I can translate between vocabulary, symbols and/or a
diagram to communicate.
MA.HS.GE.AST.01.2: I can demonstrate my understanding of the undefined terms.
MA.HS.GE.AST.01.3: I can use definitions, postulates, and theorems to build and
defend a logical argument.
MA.HS.GE.AST.01.4: I can apply inductive and deductive reasoning to build and
defend a logical argument.
MA.HS.GE.ALT.02: I can prove and apply congruence theorems dealing with angles
and lines to solve problems and justify my solutions.
MA.HS.GE.AST.02.1: I can apply and prove theorems and use properties dealing
with vertical angles and a linear pair of angles.
MA.HS.GE.AST.02.2: I can apply and prove theorems and use properties dealing
with complementary and supplementary angles.
MA.HS.GE.AST.02.3: I can apply and prove theorems and use properties dealing
with parallel and perpendicular lines.
MA.HS.GE.AST.02.4: I can use angle measures to prove that lines are parallel or
perpendicular.
MA.HS.GE.ALT.03: I can connect linear algebra and coordinates to geometric
situations and use it to prove geometric theorems. (CCSS-G-GPE-4-7)
MA.HS.GE.AST.03.1: I can use coordinates to prove simple geometric theorems
algebraically.
 For example, prove or disprove that a figure defined by four given points in the
coordinate plane is a rectangle
 Prove or disprove that the point (1, √3) lies on the circle centered at the origin and
containing the point (0, 2)
MA.HS.GE.AST.03.2: I can prove the slope criteria for parallel and perpendicular
lines and use them to solve geometric problems.
 For example, find the equation of a line parallel or perpendicular to a given line that
passes through a given point.
 Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g. find the equation of a line parallel or perpendicular to a given
line that passes through a given a point).
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 Given a diagram, determine if two lines are parallel, perpendicular, or neither.
MA.HS.GE.AST.03.3: I can find the point on a line segment between two given
points that divides the segment in a given ratio (1/2, ¼, 1/8…).
 Use midpoint theorem.
MA.HS.GE.AST.03.4: I can prove theorems about quadrilaterals (opposite sides
are congruent, opposite angles are congruent, the diagonals of a parallelograms
with congruent diagonals.
MA.HS.GE.ALT.04: I can prove and apply congruence theorems dealing with triangles
to solve problems and justify my solutions.
MA.HS.GE.AST.04.1: I can use a diagram that marks the congruent segments and
angles and determine if two triangles are congruent.
MA.HS.GE.AST.04.2: I can use a diagram that marks the congruent segments and
angles and formally prove if two triangles are congruent.
MA.HS.GE.AST.04.3: I can use Corresponding Parts of Congruent Triangles
Theorem to determine and prove other statements.
MA.HS.GE.AST.04.4: I can apply the congruence of polygons to solve problems.
MA.HS.GE.ALT.05: I am able to use a variety of tools and methods to construct basic
geometric figures.
MA.HS.GE.AST.05.1: I can draw formal geometric constructions with a variety of
tools and methods, which could include, but not limited to, the following;
compass and straightedge, string, reflective devices, and dynamic geometric
software.
 Formal Geometric Constructions should include: Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.
MA.HS.GE.AST.05.2: I can apply and construct triangle properties including
medians, centroids, circumcenters, orthocenters, and incenters.
MA.HS.GE.AST.05.3: I can construct an equilateral triangle, a square and a regular
hexagon inscribed in a circle.
MA.HS.GE.AST.05.4: I can construct the inscribed and circumscribed circles of a
triangle.
MA.HS.GE.ALT.06: I can apply the laws of similarity to solve problems and prove my
solutions
MA.HS.GE.AST.06.1: I can apply the similarity of polygons to solve problems
MA.HS.GE.AST.06.2: I can apply the triangle similarity theorems to solve
problems, write and complete proofs.
MA.HS.GE.AST.06.3: I can prove whether or not two shapes are similar.
Edited 6/25/12
MA.HS.GE.ALT.07: I can solve for unknown lengths and angles in right triangles and
justify my solutions. (CCSS-G-SRT-6-8)
MA.HS.GE.AST.07.1: Given three side lengths, I can determine and justify whether
a triangle can be created.
MA.HS.GE.AST.07.2: I can use the Pythagorean Theorem to find unknown lengths
of right triangles and determine if a triangle is right, obtuse, or acute.
MA.HS.GE.AST.07.3: I can demonstrate and use properties of special right
triangles.
 30- 60-90 triangles
 45-45-90 triangles
MA.HS.GE.AST.07.4: I can use trigonometric ratios (sine, cosine and tangent) to
find unknown lengths in right triangles.
 Explain and use the relationship between the sine and cosine of complementary angles.
 Understand that by similarity, side ratios in right triangles are properties of angles in
the triangle, leading to definitions of trigonometric ratios for acute angles.
MA.HS.GE.AST.07.5: I can use trigonometric ratios (sine, cosine, and tangent) to
find the unknown angles in right triangles.
 Explain and know the differences between; sin, sin-1 , cos, cos-1 , tan, tan-1 and when to
use them.
MA.HS.GE.AST.07.6: In applied problems I can use trigonometric ratios and the
Pythagorean Theorem to solve right triangles.
MA.HS.GE.ALT.08: I can prove theorems and utilize the properties to solve problems
of two-dimensional polygons, including real-world applications. (CCSS-G-CO-10-11,
CCSS-G-MG-1-3)
MA.HS.GE.AST.08.1: I can classify polygons based on characteristics.
 Triangle classifications: right, acute, obtuse, scalene, equilateral, isosceles.
 Quadrilateral classifications: trapezoid, rectangle, square, kite, parallelogram, and
rhombus.
 General classifications: by number of sides, by properties of quadrilaterals, equilateral,
equiangular, regular, convex, concave.
MA.HS.GE.AST.08.2: I can find the perimeter and area of a variety of polygons,
including applications.
 Including: regular polygons, quadrilaterals, triangles, composite shapes, and shaded
regions.
 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles
(e.g. using the distance formula)
 Apply concepts of density based on area and volume in modeling situations (ex: person
per square mile)
MA.HS.GE.AST.08.3: I can find the unknown sides and angles of a variety of
polygons, including applications.
 Given area or perimeter of a polygon, find a missing dimension.
 Given a diagram or information, find a missing angle.
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MA.HS.GE.AST.08.4: Given similar figures, I can compare and compute their
respective areas and volumes. *Can be taught in 2-D and 3-D.
MA.HS.GE.ALT.09: I can apply properties of circles to solve problems and justify my
solutions. (CCSS-G-C-1-5)
MA.HS.GE.AST.09.1: I can apply properties of angles formed by chords, tangents
and secants to solve problems.
 This includes the use of congruent circles, concentric circles, radius, chord, diameter,
tangent, point of tangency, central angle, inscribed angle.
MA.HS.GE.AST.09.2: I can prove that all circles are similar.
MA.HS.GE.AST.09.3: I can state and use precise definitions of circles, arcs,
degrees, radians, arc measure, arc length, and areas of sectors.
MA.HS.GE.AST.09.4: I can derive the formula for the area of a sector of a circle.
MA.HS.GE.AST.09.5: I can give an informal argument for the circumference of a
circle, and for the area of a circle.
MA.HS.GE.AST.09.6: I can use coordinates to prove that a point lies on a circle
and circumscribed and inscribed circles.
MA.HS.GE.AST.09.7: I can prove properties of angles for a quadrilateral inscribed
in a circle.
MA.HS.GE.ALT.10: I can apply the characteristics and properties of ThreeDimensional figures to solve problems, including applications and justify my
solutions. (CCSS-G-GMD-1-3, CCSS-G-MG-1-3)
MA.HS.GE.AST.10.1: I can identify and classify 3-D figures from a model, a net,
and different perspectives.
 Recognize face, vertex, edge, diagonal, lateral face, base, altitude.
 Use geometric shapes, their measures, and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a cylinder)
MA.HS.GE.AST.10.2: I can find the surface area of 3-Dimensional figures including
applications.
 Given the surface area of 3-Dimensional figures, I can find missing measures.
 Applications situations should specifically address concepts of density and optimization
as well as other situations.
MA.HS.GE.AST.10.3: I can find the volume of 3-Dimensional figures, including
applications.
 Give an informal argument for the volume of a cylinder, pyramid and cone.
 Give an informal argument using Cavalieri’s principle for the formulas for the volume of
a sphere and other solid figures.
 Given the volume area of 3-Dimensional figures, I can find missing measures.
 Apply geometric methods to solve design problems (e.g., designing an object or structure
to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios)
MA.HS.GE.AST.10.4: I can visualize relationships between 2-D and 3-D figures.
 Identify the shapes of 2-dimensional cross-sections of 3-dimensional objects, and identify
3-dimensional objects generated by rotations of 2-dimensional objects.
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MA.HS.GE.ALT.12: I can use independence and conditional probability formally to
interpret data and compute the probabilities of compound events. (CCSS-S-CP-1-7)
MA.HS.GE.AST.12.1: I can describe events as subsets of a sample space (the set of
outcomes) using characteristics (or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or”, “and”, “not”).
MA.HS.GE.AST.12.2: I can demonstrate that two events A and B are independent
of the probability of A and B occurring together is the products of their
probabilities, and use this characterization to determine if they are independent.
MA.HS.GE.AST.12.3: I can use the general formula to compute the conditional
probability of A given B as P(A and B)/P(B).
MA.HS.GE.AST.12.4: I can use a two-way table as a sample space to decide if
events are independent and to approximate conditional probabilities.
MA.HS.GE.AST.12.5: I can recognize and explain the concepts of conditional
probability and independent in every day language and every day situations.
MA.HS.GE.AST.12.6: I can model conditional probability of an event through Venn
Diagrams and Factor Trees.
MA.HS.GE.AST.12.7: I can apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A
and B), and interpret the answer in terms of the model.
Due to a reduction to the number of student contact days for 2012-13, it is recommended
that this target be included only if time allows or it is naturally integrated with another
target or targets.
MA.HS.GE.ALT 11: I can apply and analyze transformations of figures. (CCSS-G-CO-25)
MA.HS.GE.AST.11.1: I can identify lines of symmetry and distinguish between
rotation and reflection symmetries given a rectangle, parallelogram, trapezoid, or
regular polygon,
MA.HS.GE.AST.11.2: I can identify and draw rigid transformations of 2dimensional figures on and off the coordinate plane.
 Transformations should include translations, reflections across either axis, or y = +/- x,
and rotations about the origin in multiples of 90 degrees.
 Students can use graph paper, tracing paper, or geometry software to represent rigid
transformations.
MA.HS.GE.AST.11.3: I can identify and apply non-rigid transformations of
geometric figures on and off the coordinate plane.
Transformations should address scale factor, dilations including origin centered dilations,
and similarity.