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Transcript
Developing Geometric Sense
Transitions:
Coordinate Plane. Equations of lines parallel and perpendicular to each other and a given line.
Supplementary, complementary, vertical, and adjacent angles. Number patterns and inductive reasoning.
Disproving statements using counter examples. Midpoints, angle bisectors, and the bisector of a segment.
Construction of the perpendicular bisector of a line segment*
Understand
polygons and
angles
Understand
parallel lines cut
by transversals
12.0, 13.0, 16.0*
7.0, 16.0*
Standards 1.0, 2.0, 3.0
Using axioms, theorems, definitions and examples
Using inductive and deductive reasoning
Proof by contradiction
Constructing geometric proofs, logical arguments and counterexamples
• Construct the bisector of an
angle*
• Construct an angle congruent to
a given angle*
• Solve problems using angle and
side measures for triangles and
polygons
• Prove relationships between
angles in polygons
• Construct the parallel to a line
through a point not on the line*
• Prove and use properties of
parallel lines cut by a
transversal
• Construct the perpendicular
to a line from a point on the
line and from a point not on the
line*
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Triangles, Trigonometry and Quadrilaterals
Transitions:
Similarity and congruence of common geometric figures using the coordinate system Use of
the Pythagorean Theorem and its converse to find the length of the missing side of a right triangle Ratios and
proportions Roots and radicals Simple properties of common quadrilaterals and triangles Construction of
congruent triangles*
Understand triangle
congruency and
similarity
Understand the
properties of
quadrilaterals
Understand the properties of
right triangles and
trigonometry
4.0, 5.0, 6.0, 16.0*
7.0
14.0, 15.0, 16.0*, 18.0, 19.0, 20.0
Standards 1.0, 2.0, 3.0
Using axioms, theorems, definitions and examples
Using inductive and deductive reasoning
Proof by contradiction
Constructing geometric proofs, logical arguments and counterexamples
• Prove congruence of
triangles
• Apply ratios and
proportions to solving
problems
• Use the triangle inequality
• Construct the circumcircle
of a triangle*
• Prove and use
properties of
quadrilaterals
• Categorize
shapes based on
properties
• Prove the Pythagorean
Theorem
• Use the Pythagorean
Theorem to find missing
sides and distance
• Use special right triangle
properties. ( 45° , 45° , 90°
and 30°, 60°, 90° )
• Know and use
trigonometric ratios
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Circles, Area and Volume
• Transitions: Circumference, radius, diameter, and pi
Area and volume of common geometric figures
Use of coordinate graphs to plot simple figures, determine related lengths and areas, and determine their image
under translations and reflections
Ratios and proportions
Area of common geometric figures using the
coordinate system
Understand the
properties of
circles
Understand, derive
and apply area
formulas
Understand
volume and
surface area
7.0, 16.0*, 21.0
8.0, 10.0, 11.0
9.0, 11.0
Standards 1.0, 2.0, 3.0
Using axioms, theorems, definitions and examples
Using inductive and deductive reasoning
Proof by contradiction
Constructing geometric proofs, logical arguments and counterexamples
• Derive and solve problems involving
circumference and area
• Prove and solve problems about inscribed
angles, chords, secants, tangents,
inscribed and circumscribed polygons
• Construct the tangent to a circle from a
point on the circle*
• Construct the tangents to a circle from a
point not on the circle*
• Use construction to locate the center of a
circle*
• Compute area of
triangles and
quadrilaterals
• Solve problems
involving perimeter
and area
• Investigate how
dimension changes
affect perimeter and
area
• Solve problems
involving surface area
• Solve problems
involving volume
• Investigate how
dimension changes affect
volume and surface area
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Transformations and Coordinate Geometry
• Transitions: Coordinate system Use of coordinate graphs to plot simple figures, determine related
lengths and areas, and determine their image under translations and reflections Equations of lines
Understand
transformations
22.0
CST
Understand the
relationships in
coordinate geometry
17.0
Standards 1.0, 2.0, 3.0
Using axioms, theorems, definitions and examples
Using inductive and deductive reasoning
Proof by contradiction
Constructing geometric proofs, logical arguments and counterexamples
• Rotate, translate,
reflect, and
stretch figures
and objects
• Prove theorems using
elements of coordinate
geometry such as:
1) midpoint formula
2) distance formula
3) equations of
lines
4) equations of
circles
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