Hauptinhalt
Nebraska Math
High School: GEOMETRY
Students will solve problems and reason with geometry using multiple representations, make connections within math and across disciplines, and communicate their ideas.
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
- Congruent triangles & the SSS postulate/criterion
- 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
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.
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
Identify and apply right triangle relationships including converse of the Pythagorean Theorem.
Apply side and angle relationships of special right triangles (30-60-90 and 45-45-90) to solve geometric problems.
Identify and apply right triangle relationships including sine, cosine, and tangent.
- 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 word problem
- Right triangle word problems
- Sine & cosine of complementary angles
- 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
- Triangle similarity & the trigonometric ratios
- Trig challenge problem: trig values & side ratios
- 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
Apply interior and exterior angle formulas for n-gons and apply to authentic situations.
Compare/contrast the properties of quadrilaterals: parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids.
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Use slope and the distance formula to determine the type of quadrilateral.
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 & arc length
- 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
Convert between various units of volume (e.g., cubic feet to cubic yards).
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Apply the effect of a scale factor to determine the volume of similar three-dimensional shapes and solids.
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.
Derive the midpoint formula using the concept of average and apply the midpoint formula to find coordinates.
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.
Find the equation of a circle given the radius and the center.
Know and use definitions to make deductions in mathematical argumentation (e.g., syllogism, detachment).
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Evaluate the validity of conditional statements, including biconditional statements (e.g., conditional, converse, contrapositive, inverse).
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Evaluate the validity of an argument communicated in different ways (e.g., a flow format, two- column, paragraph format).
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Use coordinate geometry to prove triangles are right, acute, obtuse, isosceles, equilateral, or scalene.
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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
- Congruent triangles & the SSS postulate/criterion
- Corresponding angles in congruent triangles
- Determine congruent triangles
- Determine similar triangles: Angles
- 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: Earth & Moon radii
- 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
- Use similar & congruent triangles
- Using similar & congruent triangles
- Using similarity to estimate ratio between side lengths
- Using the angle bisector theorem
- Why SSA isn't a congruence postulate/criterion
Prove and apply geometric theorems about quadrilaterals using deductive reasoning.