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Building blocks of geometry - undefined terms and notation

Triangles - Pythag Th, Pythag Inequalities, 30-60-90, 45-45-90, trigonometry, circumscribed, inscribed, incenter, orthocenter, circumcenter, segments within (altitude, angle bisector, perp bisector), constructions

Quadrilaterals - all properties of all quads

triangle congruency ie proofs

circles - angles and segments

Logic -

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*Define terms in geometry based on point, line, distance on a line and circular arc
*transformations, rotations, reflections, dilations of figures
*writing sequences of transformations
*use theorems about lines and angles (vertical angles, corresponding angles, alternate interior, alternate exterior)
*use theorems about triangles (interior angle sum, segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, medians of a triangle meet at a point)
*use theorems about parallelograms (opposites sides and angles are congruent, diagonals of a parallelogram bisect each other, rectangles are parallelograms with congruent diagonals)
*perform formal geometric constructions to construct an equilateral triangle, square, regular hexagon inscribed in a circle
*prove triangles are similar and use properties of similarity
*use trig ratios to find side ratios in right triangles
*use trig ratios and Pythagorean Theorem to solve applied problems
*identify and describe relationships among inscribed angles, radii, and chords, central, inscribed, and circumscribed angles, inscribed angles on a diameter are right angles, radius of a circle is perpendicular to the tangent where the radius intersects the circle
*construct inscribed and circumscribed circles of a triangle
*find arc length and area of a sector and define radian measure of the angle
*use volume formulas for cylinders, pyramids, cones, and spheres to solve problems
*use coordinate geometry to solve problems
*model with geometric problems
*describe events as subsets of a sample space using union, intersection, and complement
*determine probability of independent events and given probabilities, determine if two events are independent
*solve conditional probability problems
*use the addition rule to solve compound event probabilities

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Congruence • Understand congruence in terms of rigid motions • Prove geometric theorems Similarity, Right Triangles• Understand similarity in terms of similarity transformations • Prove theorems using similarity • Define trigonometric ratios and solve problems involving right triangles Expressing Geometric Properties with Equations • Use coordinates to prove simple geometric theorems algebraically Modeling with Geometry • Apply geometric concepts in modeling situations 

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Congruence • Understand congruence in terms of rigid motions • Prove geometric theorems Similarity, Right Triangles• Understand similarity in terms of similarity transformations • Prove theorems using similarity • Define trigonometric ratios and solve problems involving right triangles Expressing Geometric Properties with Equations • Use coordinates to prove simple geometric theorems algebraically Modeling with Geometry • Apply geometric concepts in modeling situations 

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GENERAL SKILLS
- Choose a level of accuracy suitable to the problem (Significant Figures) (N.Q.3)

QUADRATICS
- Solve quadratic equations in one variable (A.REI.4)
- Use process of factoring and completing the square in a quadratic function to show zeros, extremes, symmetry and interpret in terms of the context (F.IF.8a)

FUNCTIONS
- **Compare properties of two functions represented in different ways (F.IF.9)

GEOMETRY - VOCAB AND TRANSFORMATIONS
- Use precise geometric vocabulary to describe figures (G.CO.1)
- Accurately describe and apply different transformations and whether they preserve congruence, similarity, or neither (G.CO.2, 4, 6; G.SRT.2)
- Given transformations and an original figure, construct the new figure (and v.v.) (G.CO.5)

GEOMETRY - TRIANGLES
- Triangle congruence theorems and uses (G.CO.7-8, G.SRT.3)
- Informally prove and apply theorems regarding lines, angles, triangles, and parallelograms (G.CO.9-11, G.SRT.4-5)
- Use ratios of sides of similar triangles to solve problems (G.SRT.6)

GEOMETRY - CIRCLES
- Identify and describe relationships among inscribed angles and radii (G.C.2)
- Find arc lengths and areas of sectors of circles (G.C.5)

GEOMETRY - PROOFS
- Use coordinates to prove simple geometric theorems algebraically (G.GPE.4)

GEOMETRY - LINES & POINTS
- Use slope to determine if lines are parallel/perpendicular (G.GPE.5)
- Use the distance formula to solve geometric problems (G.GPE.7)

GEOMETRY - 3D
- Give an informal argument and be able to apply the equations for the circumference of a circle, area of a circle, and volume of a cylinder/pyramid/cone/sphere AND any right prism (G.GMD.1, 3)
- Identify shapes and properties of the three-dimensional rotations of two-dimensional figures (G.GMD.4)

GEOMETRY - MODELING
- Use geometric shapes, their measures, and their properties to model objects and solve applied problems (G.MG.1-3)

PROBABILITY
- Describe events as subsets of a sample space using characteristics of the outcomes (S.CP.1)
- Understand the differences between independent and dependent events and how to calculate probabilities in both cases.  Be able to explain the differences in own words. (S.CP.1-2, 5-7)
- Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.  Use the analysis to make decisions (S.MD.5-7)

COMPLEX NUMBERS
- Identify and solve simple problems involving complex numbers (N.CN.1-2 Sort of)

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*Circles- inscribed angles, chords..	                   *Theorems for lines   *Simplify radicals       *Triangle relationships SSS, ASA..	               *independent and dependent probability	         *Conditional Probability	*Transformations in the plane	*congruence	                  *proofs of some form	       *trig relations- sine, cosine, tangent	                                *45, 45, 90 and 30,60, 90 relationships	                *parallel and perpendicular lines	                           *Some sort of proofs	*constructions- is this possible?	                       *find area length and sectors for circles	             *similarity

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*Circles- inscribed angles, chords..	                   *Theorems for lines   *Simplify radicals       *Triangle relationships SSS, ASA..	               *independent and dependent probability	         *Conditional Probability	*Transformations in the plane	*congruence	                  *proofs of some form	       *trig relations- sine, cosine, tangent	                                *45, 45, 90 and 30,60, 90 relationships	                *parallel and perpendicular lines	                           *Some sort of proofs	*constructions- is this possible?	                       *find area length and sectors for circles	             *similarity

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*angle relationships
*circle properties
*quadrilateral properties
*area, volume perimeter
*angles from a diagram (vertical, aia etc)
*triangle inequalities
*distance formula, midpoint equation of a circle
*Translations and the translation rule
*solve problems involving similar figures
*Pythagorean theorem problems to exact form
*Special right triangles
*All of the topics from ninth grade

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What Do We Want Students To Learn?

-Name points, lines, planes, segments and rays.

-Sketch intersections of lines and planes.

-Solve real-life problems involving lines and planes.

-Use the Ruler Post.

-Copy and compare segments for congruence.

-Use the Segment Addition Post.

-Find segment lengths using midpoints and segment bisectors.

-Use the Midpoint and Distance Formula.

-Classify polygons.

-Find perimeters and areas of polygons in a coordinate plane.

-Name, measure, and classify angles.

-Identify congruent angles.

-Use the Angle Addition Postulate to find angle measures.

-Bisect angles

-Identify complementary and supplementary angles.

-Identify linear and vertical angles.

What Do We Want Students To Learn?

-Write conditional & biconditional statements

-Make truth tables.

-Use inductive & deductive reasoning.

-Identify postulates using diagrams.

-Sketch and interpret diagrams

-Write two-column proofs.

-Use Algebraic Properties of Equality to justify steps in solving an equation.

-Name and prove properties of congruence.

What Do We Want Students To Learn?

-Identify & construct parallel and perpendicular lines.

--Identify pairs of angles formed by transversals.

-Prove theorems about parallel & perpendicular lines.

-Solve real-life problems using parallel and perpendicular lines.

-Use the Corresponding Angles Converse.

-Construct parallel and perpendicular lines.

-Prove Theorems about parallel lines.

-Use the Transitive Property of Equality with parallel lines.

-Identify equations of parallel and perpendicular lines.

-Write equations of parallel and perpendicular lines.

-Find distance from a point to a line.

What Do We Want Students To Learn?

-Perform translations & compositions

-Solve real-life problems involving transformations.

-Identify & perform translations, reflections, dilations, and rotations

-Identify lines of symmetry.

-Identify congruent figures.

-Describe congruence transformations.

-Solve real-life problems involving scale factors and dilations.

Perform and describe similarity transformations.

-Prove that figures are similar.

What Do We Want Students To Learn?

Classify triangles by sides and angles. Find interior and exterior angle measures of triangles.

What Do We Want Students To Learn?

-Use perpendicular bisectors to find measures. Use angle bisectors to find measures and distance relationships. Write equations for perpendicular bisectors.

-Use and find the circumcenter of a triangle. Use and find the incenter of a triangle.

-Use medians and find the centroids of triangles. Use altitudes and find the orthocenters of triangles.

-Use midsegments of triangles in the coordinate plane. Use the Triangle Midsegment Theorem to find distances.

-Write indirect proofs. List sides and angles of a triangle in order by size. Use the Triangle Inequality Theorem to find possible side lengths of triangles.

-Compare measures in triangles. Solve real-life problems using the Hinge Theorem.

What Do We Want Students To Learn?

-Use the interior & exterior angle measures of polygons.

-Use properties to find side lengths and angles of parallelograms in the coordinate plane.

-Identify and verify parallelograms.

-Use properties of special parallelograms.

-Use properties of trapezoids. Use the Trapezoid Midsegment Theorem to find distances. Use properties of kites. Identify quadrilaterals.

What Do We Want Students To Learn?

- Find corresponding lengths, perimeters and areas of similar polygons to decide if polygons are similar.

-Use the Angle-Angle, Side-Side-Side, and Side-Angle-Side Similarity Theorems.

-Use the Triangle Proportionality Theorem and its converse.

What Do We Want Students To Learn?

-Use the Pythagorean Theorem and its Converse

-Classify triangles

-Find side lengths in special right triangles & solve real-life problems involving special right triangles.

-Identify similar triangles.

- Use the tangent ratio to solve real-life problems.

-Solve real-life problems involving sine and cosine ratios.

-Use inverse trigonometric ratios. Solve right triangles.

-Use the Law of Sines & Cosines to solve triangles.

What Do We Want Students To Learn?

-Identify special segments and lines. Draw and identify common tangents.

-Find arc measures. Identify congruent arcs. Prove circles are similar.

-Use chords of circles to find lengths and arc measures

-Use inscribed angles. Use inscribed polygons.

-Find angle and arc measures. Use circumscribed angles.

-Use segments of chords, tangents, and secants.

-Write and graph equations of circles. Write coordinate proofs involving circles. Solve real-life problems using graphs of circles

What Do We Want Students To Learn?

-Use the formula for circumference. Use arc lengths to find measures. Solve real-life problems. Measure angles in radians.

-Use the formula for the area of a circle. Use the formula for population density. Find areas of sectors. Use areas of sectors.

-Find areas of rhombuses and kites. Find angle measures in regular polygons. Find areas of regular polygons.

-Classify solids. Describe cross sections. Sketch and describe solids of revolution.

What Do We Want Students To Learn?

-Find sample spaces.

-Find theoretical & experimental probabilities.

-Find geometric probability.

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What skills should students be assessed on in 10th grade? 

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What skills should students be assessed on in 10th grade? 