#### Type:

Full Course, Other

#### Description:

This is a first year, high-school level course on Geometry (which is based on Euclid's elements). It revisits many of the basic geometrical concepts studied in earlier courses, but addresses them with more mathematical rigor. There is strong focus on proving theorems and results from basic postulates.

#### Subjects:

• Mathematics > General
• Mathematics > Geometry
• Mathematics > Problem Solving
• Mathematics > Trigonometry

#### Education Levels:

• Grade 6
• Grade 7
• Grade 8
• Grade 9
• Grade 10
• Grade 11
• Grade 12
• Professional Education & Development
• Vocational Training

#### Keywords:

geometry, khan academy

English

#### Access Privileges:

Public - Available to anyone

#### License Deed:

Creative Commons Attribution Share Alike

#### Collections:

None
Update Standards?

#### MA.9-12.G.1.a: Mathematics

identifying the converse, inverse, and contrapositive of a conditional statement;

#### MA.9-12.G.1.b: Mathematics

translating a short verbal argument into symbolic form;

#### MA.9-12.G.1.c: Mathematics

using Venn diagrams to represent set relationships; and

#### MA.9-12.G.1.d: Mathematics

using deductive reasoning.

#### MA.9-12.G.2.a: Mathematics

determine whether two lines are parallel;

#### MA.9-12.G.2.b: Mathematics

verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and

#### MA.9-12.G.2.c: Mathematics

solve real-world problems involving angles formed when parallel lines are cut by a transversal.

#### MA.9-12.G.3.a: Mathematics

investigating and using formulas for finding distance, midpoint, and slope;

#### MA.9-12.G.3.b: Mathematics

applying slope to verify and determine whether lines are parallel or perpendicular;

#### MA.9-12.G.3.c: Mathematics

investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

#### MA.9-12.G.3.d: Mathematics

determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

#### MA.9-12.G.4.a: Mathematics

a line segment congruent to a given line segment;

#### MA.9-12.G.4.b: Mathematics

the perpendicular bisector of a line segment;

#### MA.9-12.G.4.c: Mathematics

a perpendicular to a given line from a point not on the line;

#### MA.9-12.G.4.d: Mathematics

a perpendicular to a given line at a given point on the line;

#### MA.9-12.G.4.e: Mathematics

the bisector of a given angle;

#### MA.9-12.G.4.f: Mathematics

an angle congruent to a given angle; and

#### MA.9-12.G.4.g: Mathematics

a line parallel to a given line through a point not on the given line.

#### MA.9-12.G.5.a: Mathematics

order the sides by length, given the angle measures;

#### MA.9-12.G.5.b: Mathematics

order the angles by degree measure, given the side lengths;

#### MA.9-12.G.5.c: Mathematics

determine whether a triangle exists; and

#### MA.9-12.G.5.d: Mathematics

determine the range in which the length of the third side must lie.

#### MA.9-12.G.6: Mathematics

The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

#### MA.9-12.G.7: Mathematics

The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.

#### MA.9-12.G.8: Mathematics

The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.

#### MA.9-12.G.9: Mathematics

The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.

#### MA.9-12.G.10: Mathematics

The student will solve real-world problems involving angles of polygons.

#### MA.9-12.G.11.a: Mathematics

investigate, verify, and apply properties of circles;

#### MA.9-12.G.11.b: Mathematics

solve real-world problems involving properties of circles; and

#### MA.9-12.G.11.c: Mathematics

find arc lengths and areas of sectors in circles.

#### MA.9-12.G.12: Mathematics

The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.
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