Learning Goal
Part of: Use coordinates to prove simple geometric theorems algebraically — 1 of 4 cluster items
Use coordinates to prove theorems
**HSG.GPE.B.4**: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, sqrt(3)) lies on the circle centered at the origin and containing the point (0, 2).
Show moreShow less
HSG.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, sqrt(3)) lies on the circle centered at the origin and containing the point (0, 2).
What you'll learn
- Place geometric figures on a coordinate plane using strategic coordinate assignments to simplify algebraic work
- Use the distance formula to verify side lengths and determine whether sides of a figure are congruent
- Use slopes to verify whether sides of a figure are parallel or perpendicular
- Construct a complete coordinate geometry proof that a given quadrilateral is a rectangle, parallelogram, rhombus, or other specific figure
- Prove or disprove that a given point lies on a circle by substituting coordinates into the circle's equation
Prerequisites
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises