Geometry | Index

Geometry is the study of shapes, angles, distance and space. You’ll also learn to prove facts about them.

The course starts with lines, angles, proofs and transformations. It goes on to triangles, polygons, similarity, right triangle trig, circles, and surface area and volume.

It’s for high school Geometry students and anyone preparing for a geometry test.

What to know first: Algebra 1, especially solving equations, slope and simplifying square roots. Basic area and circle formulas are in Pre-Algebra.

Lessons for this course are coming soon. The list below shows every planned lesson in teaching order.

Units in this course

Unit 1: Points, Lines, Planes and Angles

  1. Points, Lines and Planes (coming soon) — the building blocks of geometry and how to name them
  2. Segment Addition Postulate (coming soon) — measure segments and use congruent segments
  3. Midpoint Formula (coming soon) — find the midpoint of a segment on the coordinate plane
  4. Distance Formula (coming soon) — find the length of a segment from its endpoints
  5. Partitioning a Line Segment (coming soon) — find the point that divides a segment in a given ratio
  6. Measuring and Classifying Angles (coming soon) — measure angles, name their types and use the angle addition postulate
  7. Angle Pairs (coming soon) — complementary, supplementary and vertical angles and linear pairs
  8. Basic Constructions (coming soon) — copy and bisect segments and angles with a compass and straightedge

Unit 2: Reasoning and Proof

  1. Conditional Statements (coming soon) — write converses, inverses and contrapositives
  2. Inductive and Deductive Reasoning (coming soon) — make conjectures from patterns and reach conclusions with logic
  3. Algebraic Proofs (coming soon) — justify each step of solving an equation with properties of equality
  4. Two-Column Proofs (coming soon) — write proofs about segments and angles with statements and reasons
  5. Proving Angle Relationships (coming soon) — prove the vertical angles theorem and other angle pair theorems

Unit 3: Parallel and Perpendicular Lines

  1. Parallel Lines and Transversals (coming soon) — corresponding, alternate interior and same-side interior angles
  2. Proving Lines Parallel (coming soon) — use angle pairs to show that two lines are parallel
  3. Proofs with Perpendicular Lines (coming soon) — theorems about perpendicular lines and the distance from a point to a line

Also see: slopes and equations of parallel and perpendicular lines in Algebra 1, Unit 4.

Unit 4: Transformations

  1. Translations (coming soon) — slide a figure and describe the move with coordinates
  2. Reflections (coming soon) — flip a figure over a line
  3. Rotations (coming soon) — turn a figure around a point
  4. Compositions of Transformations (coming soon) — combine rigid motions and describe the result
  5. Dilations (coming soon) — enlarge or shrink a figure by a scale factor
  6. Symmetry (coming soon) — line symmetry and rotational symmetry

Unit 5: Triangle Congruence

  1. Triangle Angle Sum Theorem (coming soon) — the angles of a triangle add to 180 degrees, plus the exterior angle theorem
  2. Congruent Figures (coming soon) — use rigid motions and matching parts to show figures are congruent
  3. SSS and SAS Congruence (coming soon) — prove triangles congruent with three sides, or two sides and the angle between
  4. ASA, AAS and HL Congruence (coming soon) — prove triangles congruent with angle-side combinations and right triangles
  5. CPCTC (coming soon) — show that matching parts are congruent once the triangles are
  6. Isosceles and Equilateral Triangles (coming soon) — the base angles theorem and its converse

Unit 6: Relationships Within Triangles

  1. Perpendicular and Angle Bisectors (coming soon) — properties of points on perpendicular bisectors and angle bisectors
  2. Circumcenter and Incenter (coming soon) — where a triangle’s bisectors meet and what each point does
  3. Medians and Altitudes of Triangles (coming soon) — the centroid and orthocenter, and the centroid’s 2-to-1 ratio
  4. Triangle Midsegment Theorem (coming soon) — the segment joining two midpoints is parallel to the third side and half as long
  5. Triangle Inequality Theorem (coming soon) — decide whether three lengths can make a triangle, and order sides and angles
  6. Hinge Theorem (coming soon) — compare sides and angles in two triangles

Unit 7: Polygons and Quadrilaterals

  1. Interior and Exterior Angles of Polygons (coming soon) — find angle sums and single angles of any polygon
  2. Properties of Parallelograms (coming soon) — sides, angles and diagonals of parallelograms
  3. Proving a Quadrilateral Is a Parallelogram (coming soon) — the conditions that prove a shape is a parallelogram
  4. Rectangles, Rhombuses and Squares (coming soon) — properties of special parallelograms and their diagonals
  5. Trapezoids and Kites (coming soon) — properties of trapezoids, isosceles trapezoids and kites
  6. Coordinate Proofs (coming soon) — prove properties of figures placed on the coordinate plane

Unit 8: Similarity

  1. Similar Polygons (coming soon) — scale factors and similarity transformations
  2. AA Similarity (coming soon) — prove triangles similar with two pairs of congruent angles
  3. SSS and SAS Similarity (coming soon) — prove triangles similar with proportional sides
  4. Triangle Proportionality Theorem (coming soon) — a line parallel to one side splits the other two sides proportionally
  5. Triangle Angle Bisector Theorem (coming soon) — an angle bisector divides the opposite side in the ratio of the other two sides

Unit 9: Right Triangles and Trigonometry

  1. Pythagorean Theorem (coming soon) — find a missing side of a right triangle
  2. Converse of the Pythagorean Theorem (coming soon) — use the sides to tell whether a triangle is right, acute or obtuse
  3. Special Right Triangles (coming soon) — side ratios in 45-45-90 and 30-60-90 triangles
  4. Similar Right Triangles (coming soon) — the altitude to the hypotenuse and the geometric mean
  5. Trigonometric Ratios (coming soon) — sine, cosine and tangent in right triangles (SOH CAH TOA)
  6. Solving Right Triangles (coming soon) — find missing sides and angles with trig ratios and inverse trig
  7. Angles of Elevation and Depression (coming soon) — solve height and distance problems with right triangle trig

Also see: the law of sines and law of cosines in Trigonometry, Unit 8.

Unit 10: Circles

  1. Parts of a Circle (coming soon) — radius, diameter, chords, secants and tangents
  2. Tangents to a Circle (coming soon) — why a tangent meets the radius at a right angle, and tangent segment rules
  3. Arcs and Central Angles (coming soon) — measure arcs and use central angles
  4. Inscribed Angles (coming soon) — inscribed angles, intercepted arcs and shapes inscribed in circles
  5. Angle Relationships in Circles (coming soon) — angles formed by chords, secants and tangents
  6. Segment Relationships in Circles (coming soon) — lengths of intersecting chords, secants and tangents
  7. Arc Length (coming soon) — find the length of an arc from its central angle
  8. Area of a Sector (coming soon) — find the area of a slice of a circle
  9. Equation of a Circle (coming soon) — write and graph a circle from its center and radius

Unit 11: Area, Surface Area and Volume

  1. Area of Regular Polygons (coming soon) — use the apothem and perimeter to find the area of a regular polygon
  2. Cross Sections (coming soon) — shapes made by slicing solids, and solids formed by rotating shapes
  3. Surface Area of Prisms and Cylinders (coming soon) — add the areas of all faces and curved surfaces
  4. Surface Area of Pyramids and Cones (coming soon) — use slant height to find surface area
  5. Volume of Prisms and Cylinders (coming soon) — multiply the area of the base by the height
  6. Volume of Pyramids and Cones (coming soon) — find volume as one-third of base area times height
  7. Surface Area and Volume of Spheres (coming soon) — use the radius to find a sphere’s surface area and volume
  8. Similar Solids (coming soon) — how a scale factor changes surface area and volume

Also see: Area of Triangles and Circumference and Area of Circles (Pre-Algebra, Unit 6).

For Teachers: Standards Alignment

Lessons follow the Common Core high school Geometry standards: congruence, similarity, right triangle trig, circles, coordinate geometry, measurement and modeling. Slopes of parallel and perpendicular lines are taught in Algebra 1. The laws of sines and cosines are in Trigonometry, and probability is in Statistics.

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