30 written chapters · 1 published teaching videos

Grade 10, one chapter at a time.

Bring algebra and geometry into the same conversation. Explore transformations, similarity, functions, and probability with attention to the conditions under which a result is valid.

Watch teaching clips Open the study guide

Watch, understand, then try it

Watch this grade’s teaching clips

Short explanations with animated examples, captions, and a full transcript. Each video opens beside its matching practice question so you can try the idea yourself.

16 sec
Grade 10 · AI-assisted teaching
Right triangles: six, eight, ten
AI-assisted presenter with an American male AI voice. Use the Pythagorean relationship for a right triangle with legs six and eight. Their squared lengths add to 100, so the longest side is ten.
Watch and practice

Explore the complete written study sequence

1 short teaching clip is available above, each linked to its exact practice question. Every chapter below opens a written lesson with worked examples and practice. Full lesson recordings are being prepared; the interactive animations are available now.

Explore this level’s 100 interactive animations

Follow the learning sequence

Chapters and video availability

Each chapter follows an existing academy lesson. Numbers match the written study order; grade placement is a guide and school sequences may vary.

With a teaching video

30 of 30 chapters · in study order

Chapter 1 · Geometry
Disprove a universal claim with one example
Distinguish a confirming example from a decisive counterexample.
Written lesson available · video pending
Study this chapter
Chapter 2 · Geometry
A true statement need not have a true converse
Distinguish a conditional, its converse, and its contrapositive.
Written lesson available · video pending
Study this chapter
Chapter 3 · Geometry
Prove the triangle angle sum with a parallel line
Use alternate interior angles to justify the Euclidean triangle sum.
Written lesson available · video pending
Study this chapter
Chapter 4 · Geometry
Use an included angle in a congruence argument
Apply side-angle-side when the angle lies between the known sides.
Written lesson available · video pending
Study this chapter
Chapter 5 · Trigonometry
See why side-side-angle can give two triangles
Use sine symmetry to identify two valid triangle configurations.
Written lesson available · video pending
Study this chapter
Chapter 6 · Geometry
Use angle agreement to scale triangles
Apply AA similarity and match corresponding sides.
Written lesson available · video pending
Study this chapter
Chapter 7 · Geometry
Dilate from a center other than the origin
Scale a displacement from a specified dilation center.
Written lesson available · video pending
Study this chapter
Chapter 8 · Geometry
Derive a rotation from two intersecting reflections
Explain why two reflections in intersecting lines produce a rotation by twice their oriented angle.
Written lesson available · video pending
Study this chapter
Chapter 9 · Geometry
Two parallel reflections create a translation
Track a point through two reflections in parallel lines.
Written lesson available · video pending
Study this chapter
Chapter 10 · Geometry
Find the possible lengths of a third side
Use strict triangle inequalities to describe a feasible interval.
Written lesson available · video pending
Study this chapter
Chapter 11 · Geometry
Connect midpoints to find a half-size parallel segment
Derive a triangle midsegment's direction and length.
Written lesson available · video pending
Study this chapter
Chapter 12 · Geometry
Locate the centroid along a median
Use the two-to-one division of a triangle's medians.
Written lesson available · video pending
Study this chapter
Chapter 13 · Geometry
Find points equally distant from two endpoints
Derive a perpendicular bisector as an equidistance locus.
Written lesson available · video pending
Study this chapter
Chapter 14 · Geometry
Connect a circle's central and inscribed angles
Use the intercepted arc to compare circle angles.
Written lesson available · video pending
Study this chapter
Chapter 15 · Geometry
Use the right angle at a tangent point
Apply the tangent-radius perpendicular relation and Pythagoras.
Written lesson available · video pending
Study this chapter
Chapter 16 · Geometry
Use the same turn fraction for arc and sector
Find arc length and sector area from a central angle in degrees.
Written lesson available · video pending
Study this chapter
Chapter 17 · Geometry
Derive distance from horizontal and vertical changes
Use the Pythagorean theorem for the distance between two planar points.
Written lesson available · video pending
Study this chapter
Chapter 18 · Geometry
Prove a quadrilateral is a parallelogram with midpoints
Use diagonal bisection as a coordinate criterion.
Written lesson available · video pending
Study this chapter
Chapter 19 · Geometry
Split a right triangle into similar triangles
Use similarity to relate an altitude to hypotenuse segments.
Written lesson available · video pending
Study this chapter
Chapter 20 · Trigonometry
Choose sine, cosine, or tangent from the known sides
Match a right-triangle ratio to a chosen reference angle.
Written lesson available · video pending
Study this chapter
Chapter 21 · Trigonometry
Recover an angle from a measured ratio
Use an inverse trigonometric function with consistent angle units.
Written lesson available · video pending
Study this chapter
Chapter 22 · Trigonometry
Extend Pythagoras to a nonright triangle
Use the cosine rule with an included angle.
Written lesson available · video pending
Study this chapter
Chapter 23 · Trigonometry
Use a known opposite side-angle pair
Match corresponding sides and opposite angles in the sine rule.
Written lesson available · video pending
Study this chapter
Chapter 24 · Trigonometry
Find area without a stated altitude
Express a triangle's height using sine of the included angle.
Written lesson available · video pending
Study this chapter
Chapter 25 · Geometry
Separate length, area, and volume scale factors
Apply squared and cubed scaling to similar figures and solids.
Written lesson available · video pending
Study this chapter
Chapter 26 · Geometry
Subtract similar cones to find a frustum's volume
Use similarity and volume subtraction for a cone cut by a plane parallel to its base.
Written lesson available · video pending
Study this chapter
Chapter 27 · Geometry
Unroll a cone to find its covering area
Use slant height for a cone's lateral surface area.
Written lesson available · video pending
Study this chapter
Chapter 28 · Statistics
Change the denominator when a condition is given
Calculate a conditional relative frequency from a two-way count table.
Written lesson available · video pending
Study this chapter
Chapter 29 · Statistics
A larger sample can still miss the population
Distinguish sample size from representativeness.
Written lesson available · video pending
Study this chapter
Chapter 30 · Statistics
Measure how far an observation is from a fitted line
Compute a signed residual and distinguish interpolation from extrapolation.
Written lesson available · video pending
Study this chapter

Watch this grade’s teaching clips

Right triangles: six, eight, ten

Explore the complete written study sequence

Chapters and video availability

Disprove a universal claim with one example

A true statement need not have a true converse

Prove the triangle angle sum with a parallel line

Use an included angle in a congruence argument

See why side-side-angle can give two triangles

Use angle agreement to scale triangles

Dilate from a center other than the origin

Derive a rotation from two intersecting reflections

Two parallel reflections create a translation

Find the possible lengths of a third side

Connect midpoints to find a half-size parallel segment

Locate the centroid along a median

Find points equally distant from two endpoints

Connect a circle's central and inscribed angles

Use the right angle at a tangent point

Use the same turn fraction for arc and sector

Derive distance from horizontal and vertical changes

Prove a quadrilateral is a parallelogram with midpoints

Split a right triangle into similar triangles

Choose sine, cosine, or tangent from the known sides

Recover an angle from a measured ratio

Extend Pythagoras to a nonright triangle

Use a known opposite side-angle pair

Find area without a stated altitude

Separate length, area, and volume scale factors

Subtract similar cones to find a frustum's volume

Unroll a cone to find its covering area

Change the denominator when a condition is given

A larger sample can still miss the population

Measure how far an observation is from a fitted line