Nebraska Math
Students will solve problems and reason with geometry using multiple representations, make connections within math and across disciplines, and communicate their ideas.
HS.G.1Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create two- dimensional shapes.
HS.G.1.a
Demonstrate that two figures are similar or congruent by using a sequence of rigid motions and dilations that map a figure onto the other in problems both with and without coordinates.
- Angle congruence equivalent to having same measure
- Justify triangle congruence
- Proofs with transformations
- Proofs with transformations
- Proving the ASA and AAS triangle congruence criteria using transformations
- Proving the SAS triangle congruence criterion using transformations
- Proving the SSS triangle congruence criterion using transformations
- Segment congruence equivalent to having same length
HS.G.1.b
Describe symmetries of a figure in terms of rigid motions that map a figure onto itself and make inferences about symmetric figures (e.g., unknown side lengths or angle measures) in problems both with and without coordinates.
- Finding a quadrilateral from its symmetries
- Finding a quadrilateral from its symmetries (example 2)
HS.G.1.c
Explain how the criteria for triangle congruence and similarity (ASA, SAS, and AAS SSS congruence; AA similarity criterion) follow from the definition of congruence and similarity in terms of corresponding parts.
- Proving the ASA and AAS triangle congruence criteria using transformations
- Proving the SAS triangle congruence criterion using transformations
- Proving the SSS triangle congruence criterion using transformations
- Triangle congruence postulates/criteria
- Triangle congruence review
- Triangle similarity postulates/criteria
HS.G.1.d
Identify and apply right triangle relationships including converse of the Pythagorean Theorem.
- Getting ready for right triangles and trigonometry
- Multi-step word problem with Pythagorean theorem
- Pythagorean theorem challenge
- Using right triangle ratios to approximate angle measure
HS.G.1.e
Apply side and angle relationships of special right triangles (30-60-90 and 45-45-90) to solve geometric problems.
- 30-60-90 triangle example problem
- Special right triangles
- Special right triangles review
HS.G.1.f
Identify and apply right triangle relationships including sine, cosine, and tangent.
- Cosine equation algebraic solution set
- Cosine equation solution set in an interval
- Cosine, sine and tangent of π/6 and π/3
- Hypotenuse, opposite, and adjacent
- Intro to inverse trig functions
- Relate ratios in right triangles
- Right triangle trigonometry review
- Right triangle trigonometry word problems
- Right triangle word problem
- Solve for a side in right triangles
- Solve for an angle in right triangles
- Solving for a side in right triangles with trigonometry
- Solving for a side in right triangles with trigonometry
- Trig identities from reflections and rotations
- Trig values of π/6, π/4, and π/3
- Trig word problem: complementary angles
- Trigonometric ratios in right triangles
- Trigonometric ratios in right triangles
- Trigonometric ratios in right triangles
- Using complementary angles
HS.G.1.g
Apply interior and exterior angle formulas for n-gons and apply to authentic situations.
- Getting ready for congruence
HS.G.1.h
Compare/contrast the properties of quadrilaterals: parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids.
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HS.G.1.i
Use slope and the distance formula to determine the type of quadrilateral.
- Classify figures by coordinates
- Classifying figures with coordinates
- Classifying quadrilaterals on the coordinate plane
HS.G.1.j
Identify, describe, apply, and reason through properties of central angles, inscribed angles, angles formed by intersecting chords, secants, and/or tangents to find the measures of angles related to the circle, arc lengths, and areas of sectors.
- Arc length
- Arc length as fraction of circumference
- Arc length from subtended angle
- Arc length from subtended angle: radians
- Area of a sector
- Area of a sector
- Challenge problems: Arc length (radians) 1
- Challenge problems: Arc length (radians) 2
- Challenge problems: Arc length 1
- Challenge problems: Arc length 2
- Challenge problems: Inscribed angles
- Challenge problems: Inscribed shapes
- Determining tangent lines: angles
- Determining tangent lines: lengths
- Geometry proof problem: squared circle
- Inscribed angle theorem proof
- Inscribed angle theorem proof
- Inscribed angles
- Inscribed angles
- Inscribed shapes
- Inscribed shapes: angle subtended by diameter
- Inscribed shapes: find inscribed angle
- Proof: perpendicular radius bisects chord
- Proof: radius is perpendicular to a chord it bisects
- Proof: Radius is perpendicular to tangent line
- Proof: Right triangles inscribed in circles
- Radians as ratio of arc length to radius
- Solving inscribed quadrilaterals
- Subtended angle from arc length
- Tangents of circles problem (example 1)
- Tangents of circles problem (example 2)
- Tangents of circles problems
HS.G.2Attributes: Students will identify and describe geometric attributes, apply properties and theorems and create three-dimensional shapes.
HS.G.2.a
Convert between various units of volume (e.g., cubic feet to cubic yards).
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HS.G.2.b
Apply the effect of a scale factor to determine the volume of similar three-dimensional shapes and solids.
- Use related volumes
- Using related volumes
HS.G.2.c
Determine surface area and volume of pyramids, as well as solids that are composites of pyramids, prisms, spheres, cylinders, and cones, using formulas and appropriate units.
- Apply volume of solids
- Interpret units in formulas
- Interpreting units in formulas
- Use related volumes
- Volume formulas review
- Volume of a pyramid or cone
- Volume of composite figures
- Volume of prisms and pyramids
- Volume of pyramids intuition
HS.G.3Coordinate Geometry and Transformations: Students will demonstrate and represent location, orientation, and relationships on the coordinate plane.
HS.G.3.a
Derive the midpoint formula using the concept of average and apply the midpoint formula to find coordinates.
- Midpoint formula
- Midpoint formula
- Midpoint formula
- Midpoint formula review
HS.G.3.b
Find the images and preimages of transformations of a point, shape, or a relation on the coordinate plane. Transformations include the following and their compositions: reflections across horizontal and vertical lines and the lines y=x and y=-x, rotations about the origin of 90 degrees, dilations about the origin by any positive scale factor, and any translation.
- Dilating shapes: shrinking
- Properties of translations
- Rotate points
- Rotate shapes
- Rotating shapes
- Rotating shapes
- Translation challenge problem
HS.G.3.c
Find the equation of a circle given the radius and the center.
- Circle equation review
- Write standard equation of a circle
- Writing standard equation of a circle
HS.G.4Logic and Proof: Students will use geometric definitions and theorems to reason abstractly and quantitatively.
HS.G.4.a
Know and use definitions to make deductions in mathematical argumentation (e.g., syllogism, detachment).
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HS.G.4.b
Evaluate the validity of conditional statements, including biconditional statements (e.g., conditional, converse, contrapositive, inverse).
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HS.G.4.c
Evaluate the validity of an argument communicated in different ways (e.g., a flow format, two- column, paragraph format).
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HS.G.4.d
Use coordinate geometry to prove triangles are right, acute, obtuse, isosceles, equilateral, or scalene.
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HS.G.4.e
Prove and apply geometric properties and theorems regarding triangles, congruence, and similarity using deductive reasoning.
- Angle-angle triangle similarity criterion
- Calculating angle measures to verify congruence
- Challenging similarity problem
- Corresponding angles in congruent triangles
- Determine congruent triangles
- Determine similar triangles: AA
- Determine similar triangles: SSS
- Determining congruent triangles
- Determining similar triangles
- Dilating triangles: find the error
- Exploring medial triangles
- Find angles in congruent triangles
- Geometry proof problem: congruent segments
- Geometry word problem: a perfect pool shot
- Geometry word problem: the golden ratio
- Intro to angle bisector theorem
- Intro to triangle similarity
- Justify triangle congruence
- Proof: Parallel lines divide triangle sides proportionally
- Proofs concerning equilateral triangles
- Proofs concerning isosceles triangles
- Prove theorems using similarity
- Prove triangle congruence
- Prove triangle properties
- Prove triangle similarity
- Proving the ASA and AAS triangle congruence criteria using transformations
- Proving the SAS triangle congruence criterion using transformations
- Proving the SSS triangle congruence criterion using transformations
- Proving triangle congruence
- Proving triangle medians intersect at a point
- Solve similar triangles (advanced)
- Solve similar triangles (basic)
- Solve triangles: angle bisector theorem
- Solving similar triangles
- Solving similar triangles: same side plays different roles
- Triangle congruence postulates/criteria
- Triangle congruence review
- Triangle similarity postulates/criteria
- Triangle similarity review
- Use ratios in right triangles
- Using similarity to estimate ratio between side lengths
- Using the angle bisector theorem
- Why SSA isn't a congruence postulate/criterion
HS.G.4.f
Prove and apply geometric theorems about quadrilaterals using deductive reasoning.
- Proof: Diagonals of a parallelogram
- Proof: Opposite angles of a parallelogram
- Proof: Opposite sides of a parallelogram
- Proof: Rhombus area
- Proof: Rhombus diagonals are perpendicular bisectors
- Proof: The diagonals of a kite are perpendicular
- Prove parallelogram properties
