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G-GPE.4 Warmup M1-044-A09-V01

Use coordinates, distance, and algebra to prove or disprove simple geometric statements.

Use coordinates to decide whether three points form an isosceles triangle

Problem

Use coordinates to decide whether points \(A(0,~0)\), \(B(4,~0)\), and \(C(2,~3)\) form an isosceles triangle.

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What this problem is really about

Translate the classification into its defining measurement: an isosceles triangle needs at least one pair of equal side lengths, not three equal sides. Compare squared distances for the three edges to avoid radicals, and also make sure the points are noncollinear so the equal measurements belong to a genuine triangle.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
G-GPE.4
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Problem type
Use coordinates to decide whether three points form an isosceles triangle