Problem preview

G-GPE.4 Warmup M2-043-A12-V04

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Complete a coordinate proof from calculated evidence

Problem

Calculated slopes for \(EF\) and \(GH\) are \(-3\) and \(1/3\). Verify their negative-reciprocal relation or product, state the applicable slope theorem, and complete the line conclusion.

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Therefore the diagonals bisect each other because the slopes are opposites.

Therefore EF is perpendicular to GH because their slopes are negative reciprocals.

Therefore EF is congruent to GH because their slopes are related.

Therefore EF is parallel to GH because both slopes involve 3.

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Curriculum context

Course: Math II
Standard: G-GPE.4
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Use coordinates to prove simple geometric theorems, including simple circle theorems.
Problem type: Complete a coordinate proof from calculated evidence