Problem preview

G-CO.12 Warmup M1-035-A04-V04

Perform formal constructions with compass/straightedge, paper folding, string, reflective devices, or geometry software.

Find a midpoint using construction reasoning

Problem

Use the displayed perpendicular-bisector construction to identify the midpoint of \(RS\) and justify it from the point's incidence and equal distances to \(R\) and \(S\).

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One of the arc-intersection points is the midpoint of RS because those points are used to draw the perpendicular bisector.

Point T is the midpoint of RS because it lies on RS and on the perpendicular bisector, so TR = TS.

Any point on the perpendicular bisector is the midpoint of RS because points on that line are equidistant from R and S.

Point R is the midpoint of RS because it is an endpoint of the segment used in the construction.

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Curriculum context

Course: Math I
Standard: G-CO.12
Category: Geometry
Domain: Congruence
Objective: Perform formal constructions with compass/straightedge, paper folding, string, reflective devices, or geometry software.
Problem type: Find a midpoint using construction reasoning