Geometry

Welcome to Common Core Regents Geometry!

SGI is now open every Tuesday during 9th period; Wednesday during 9th and 10th period in the computer lab Room 109. Please feel free to come to work on your homework or to ask any questions.

Please join me in welcoming our new SGI T.A.

Andreas Vasiliadis (Wednesday 9th period)

Aparna Saha (Wednesday 9th period)

Please return your textbook next Monday (6/10)!

Click here to see Common Core Geometry Regents Exam Room Assignments

Exam #12 - Transformations is scheduled on May 24th

(You must bring a graphing calculator, a straightedge, and a compass to this exam. If you come to the exam unprepared, 10 class participation points will be deducted for each missing item.)

It mainly focus on the following topics:

1. Translation, glide reflection.

2. Line reflection, point reflection.

3. Rotation (90, 180, 270).

4. Isometries, rigid motions.

5. Dilations.

6. Compositions of transformations.

7. Prove using compositions of transformations.

8. Constructing line of reflection, image of a graph in a point reflection, and image of a graph in dilation, etc.

9. Symmetries (point, line, rotational).

10. Use transformations to prove two geometric shapes congruent or similar.

Exam #11 Review Sheet Solution - (link closed)

Exam #11 - Coordinate Geometry is scheduled on May 10th

(You must bring a graphing calculator to this exam. If you come to the exam unprepared, 10 class participation points will be deducted for each missing item.)

It mainly focus on the following topics:

1. Finding coordinates of points, locating points.

2. Find the slope of a given lines. Determine whether two lines are parallel, perpendicular, or neither.

3. Determine whether three points are colinear.

4. Graph a line given a linear equation.

5. Write an equation for any given line using various forms (slope-intercept, point-slope, intercept, two points, etc.).

6. Find the distance of two given points.

7. Find the midpoint of a line segment. Find the equation of the perpendicular bisector of the given line segment.

8. Find the coordinate of a point that divide a line segment in certain ratio.

9. Prove statements using coordinate geometry.

10. Solving systems of linear equations.

11. Graph a circle given its equation (finding its center and radius).

12. Write an equation of a given circle.

13. Convert the equation of a circle from general form to center radius form.

14. Find the perimeter or area of a polygon on the Cartesian plane.

Exam #10 Review Sheet Solution: (link closed)

Exam #10 - Solid Geometry is scheduled on April 12th

(You must bring a graphing calculator to this exam. If you come to the exam unprepared, 10 class participation points will be deducted for each missing item.)

The exam mainly focus on (but not limited to) the following topics:

1. Relations between points, lines, and planes in space.

2. Parallel and Perpendicular lines and planes.

3. Identify common solids prisms, cylinders, pyramids, cones, spheres.

4. Finding lateral areas, total areas (surface areas), and volumes of prisms, cylinders, pyramids, cones, spheres.

5. Cross-sections of different solids.

6. Generating solids by rotating a 2-dimensional object.

7. Unerstanding the Cavalieri's principle (Click to view).

8. Modeling using 3D figures.

9. Density

10. Ratios of two similar solids.

11. Calculate the parameters of a solid inscribed in a sphere.

Exam #9 Review Sheet Solution: (link closed)

Exam #9 - Circles is scheduled on March 29th

(Please bring a graphing calculator to this exam if you want to use it.)

The exam mainly focus on (but not limited to) the following topics:

1. Terms related to a circle.

2. Convert between degrees and radians.

3. Basic theorems related to tangents, chords, and arcs.

4. Angles related to a circle.

5. Segments related to a circle.

6. Area of a sector

7. Length of an arc

8. Applications and proofs related to circles

Exam #8 Review Sheet Solution: (link closed)

Exam #8 - Similar Polygons and Areas of Polygons is scheduled on March 8th

(You must bring a graphing calculator to this exam. If you come to the exam unprepared, 10 class participation points will be deducted for each missing item.)

The exam mainly focus on (but not limited to) the following topics:

1. Ratios, proportions, unit conversions, geometry means.

2. Properties of similar polygons, similar triangles.

3. Proving two triangles are similar.

4. Ratios of corresponding sides, angle bisectors, medians, altitudes, perimeters, and areas.

5. Triangle proportionality theorem.

6. Triangle angle-bisector theorem.

7. Right Triangle Altitude Theorem.

8. Pythagorean theorem, its converse, Pythagorean triples.

9. Special right triangles: 45°-45°-90° and 30°-60°-90°.

10. Sine, cosine, and tangent ratios.

11. Inverse trigonometric functions.

12. Trig applications, angles of elevation and depression.

Exam #7 - Introduction to Constructions is scheduled on February 8th

(You must bring a straightedge and a compass to this exam. If you come to the exam unprepared, 10 class participation points will be deducted for each missing item.)

The exam mainly focus on (but not limited to) the following topics:

1. Copying line segments (including adding and subtracting line segments).

2. Copying angles (including adding and subtracting angles).

3. Bisecting line segments (or finding perpendicular bisectors) and angles.

4. Constructing a perpendicular through a point on a given line or outside of a given line.

5. Copying a triangle.

6. Constructing equilateral triangle.

7. Constructing parallel lines.

8. Construct altitudes and medians of triangles.

9. Construct equilateral triangles, squares, regular hexagons (6 sides), regular octagons (8 sides), and regular dodecagons (12 sides).

10. Find the incenter, circumcenter, centroud, orthocenter of a given triangle.

11. Theorem: the medians of a triangle intersect in a point that is two thirds of the distance form each vertex to the midpoint of the opposite side.

12. Construct a circumscribed and/or inscribed circle of a triangle.

Uniform Midyears Week Schedule: (link closed)

Exam #6 - Quadrilaterals is scheduled on December 21st

The exam mainly focus on (but not limited to) the following topics:

1. Theorems and properties of parallelograms.

2. Theorems and properties of rectangles.

3. Theorems and properties of rhombuses.

4. Theorems and properties of squares.

5. Theorems and properties of trapezoid.

6. Theorems and properties of parallel lines.

7. Proofs related to quadrilaterals.

8. Theorems and proofs related to Mid-segments of triangles and trapezoids.

9. Find the areas of quadrilaterals or polygons.

Exam #5 - Inequalities is scheduled on November 30th

The exam mainly focus on (but not limited to) the following topics:

1. Properties of inequalities.

2. The relations between angles and sides in a triangle.

3. Perpendicular segment is the shortest segment from a given point to a given line or a given plane.

4. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

5. Triangle Inequality.

6. Proofs related to the topics above.

Exam #4 - Congruent Triangles is scheduled on November 16th

(You may use a graphing calculator in this exam. your must clear your graphing calculator memory at the beginning of the exam period. Calculator memory clearing instructions)

The exam mainly focus on (but not limited to) the following topics:

1. Congruent polygons;

2. Postulate and theorems for congruent triangles. (Remember SSA does NOT ensure to two triangles congruent.)

3. Corresponding parts of congruent triangles are congruent.

4. Isosceles triangle theorems and its converse. Equilateral triangles are equiangular and its converse.

5. Proofs using congruent triangles and parallel lines

6. Proofs involves overlapping triangles and double triangle.

7. Equidistance Theorems.

8. Median, Angle bisector and Altitude.

9. The median, angle bisector and altitude drawn to the base of an isosceles triangle are identical.

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Exam #3 Review Sheet solution - (link closed)

Exam #3 - Parallel Lines is scheduled on October 26th

(You may use a graphing calculator in this exam)

The exam mainly focus on (but not limited to) the following topics:

1. Definitions of perpendicular lines, parallel lines, skew lines, and transversals;

2. Properties of parallel lines (corresponding angles, alternate interior angles, same-side interior angles, etc.);

3. Determine whether two lines are parallel;

4. Proofs related to parallel lines, special angles, and perpendicular lines;

5. Find measures of angles using parallel lines, special angles, and perpendicular lines;

6. Using auxiliary lines when needed;

7. Proofs related to triangles and polygons;

8. Find measures of angles using properties of triangles and polygons;

Exam #2 - Geometry as a Postulational System is scheduled on October 12th

The exam mainly focuses on (but not limited to) the following topics:

1. Undefined Terms;

2. Definitions and Symbols of Different Geometric Terms;

3. Postulates;

4. Equivalence Relations;

5. Collinear and Coplanar Points;

6. Congruent Line Segments and Angles;

7. Midpoint and Bisector;

8. Classification of Angles;

9. Special Pairs of Angles (Adjacent, Complementary, Supplementary, Vertical, Linear Pairs, Orthogonal Pairs);

10. Perpendicular lines;

11. Using Postulates and Theorems to Write Proofs.

Exam #1 - Logic is scheduled on Friday 9/28

The exam mainly focuses on the following topics:

• Negation;

• Conjunction; Disjunction;

• Conditional;

• Converse, Biconditional, Inverse;

• Tautology, Contradiction, Logical Equivalence;

• Constructing Truth Table

• Law of Detachment, Modus Tollens

• The Chain Rule

• Law of Disjunctive Inference, Law of Conjunctive Simplification

• Law of Conjunction, Law of Disjunctive Addition

• Contrapositive; De Morgan's Law

• Direct Proof and Indirect Proof