Problem preview

G-GPE.4 Warmup M2-043-A10-V02

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

Disprove a claim with a specified coordinate calculation

Problem

Disprove the claim that segments \(AB\) and \(CD\) are congruent when \(AB~=~5\) and \(CD~=~\sqrt{20}\). Compare their exact squared lengths, identify the failed equality condition, and state the counterconclusion.

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√20 rounds to 5, so the segments are congruent.

AB = 5 and CD = √20 = 5, so the segments are congruent.

AB² = 25 and CD² = 20, so AB and CD are not congruent.

Both lengths are positive, so the segments are congruent.

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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: Disprove a claim with a specified coordinate calculation