Geometry

Welcome to Common Core Regents Geometry!

Online Learning

The rest of the lessons will be conducted on Google Classroom.

Exam #8 Review Sheet Solution: (link)

Exam #8 - Similar Polygons and Areas of Polygons is scheduled on March 6th

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

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.

2020 Midyear Information

Midyear Schedule

Geometry Room Assignment:

Chen. PD 1. Room 202

Chen. PD 8. Room 213

You must bring a regents exams permitted graphing calculator (such as TI-83 or TI-84). If you have problem getting a graphing calculator, please let me know no later than 1/16.

Exam #6 Review Sheet Solution (Closed)

Exam #6 - Quadrilaterals is scheduled on December 20th

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 December 6th

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.

7. Theorems and properties of parallelograms.

Exam #4 - Congruent Triangles is scheduled on November 15th

(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. Median, Angle bisector and Altitude.

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

9. Equidistance Theorems.

2019-2020 Parent-Teacher Conference

Mr. Chen - Room 102

Exam #3 Review Sheet Solution: (Closed)

Exam #3 - Parallel Lines is scheduled on October 25th

(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;

Columbia Educational Outreach is hosting Columbia Splash again this year on October 27th, 2019. Classes are open to grade 8-12 students and are taught by Columbia students and alumni. Check out this website for more information: https://columbia.learningu.org

Exam #2 Review Sheet Solution: (closed)

Exam #2 - Geometry as a Postulational System is scheduled on October 11th

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 Review Sheet Solution: (closed)

Exam #1 - Logic is scheduled on Friday September 27

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