Scale Coordinates from the Origin
A dilation centered at the origin multiplies both coordinates by the same scale factor.
About 20 minutes, plus any extended practice
Open lesson 1Dilations and Right-Triangle Structure
Dilations change lengths by a common factor and preserve shape. Right-triangle relationships connect squared perpendicular lengths; their converse tests whether supplied side lengths support a right angle, including in a three-dimensional diagonal model.
Before you begin
- Evaluate squares and positive square roots; read coordinates; know legs and hypotenuse.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Subtract Squares to Recover a Leg
The hypotenuse square equals the sum of leg squares.
About 20 minutes, plus any extended practice
Open lesson 2Test a Right Angle from Three Sides
For a valid triangle, equality between the largest side’s square and the sum of the other two squares establishes a right angle opposite the largest side.
About 20 minutes, plus any extended practice
Open lesson 3Combine Two Perpendicular Right-Triangle Models
A box’s base diagonal and height form a second right triangle.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Dilations and Right-Triangle Structure
These references informed the topic selection. They do not certify complete standards alignment.