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Mathable Smart Lab

TRACK 2 • GEOMETRY Strand: Constructions, Symmetry and Tilings

Constructions and Tilings Smart Lab

Use ruler-and-compass ideas to construct perpendicular bisectors, 90° and 60° angles, angle bisectors, parallel lines, arches, hexagons, and tiling designs.

What are Geometric Constructions?

Geometric constructions use simple tools—an unmarked ruler and a compass—to create exact shapes using reasoning, arcs, equal distances and congruence.

Perpendicular bisector: A line that divides a segment into two equal parts and meets it at \(90^\circ\).
Angle bisection: Dividing an angle into two equal angles using equal arcs.
Tilings and designs: Repeating constructed units, such as petals, arches and hexagons, can create symmetric patterns.

Move the radius slider. The arc intersections above and below the segment define the perpendicular bisector.

Rules Hub

Perpendicular Bisector

Draw equal-radius arcs from both endpoints of a segment. Join the arc intersections.

90° at a Point

Mark equal points \(X\) and \(Y\) on a line around \(O\), then construct the perpendicular bisector of \(XY\).

Angle Bisector

Mark equal distances on both arms of an angle, draw equal arcs, then join the vertex to the arc intersection.

Copy an Angle

Use an arc to create a triangle on the original angle, then transfer the same lengths to the new ray.

Parallel Line

Copy a corresponding angle using ruler and compass; equal corresponding angles give parallel lines.

Regular Hexagon

Six congruent equilateral triangles meet around a point. Each central angle is \(60^\circ\).

Guided Solve Lab

Score: 0Current Streak: 🔥 0Badge: Construction Explorer


Activity Zone

🎛️ Perpendicular Bisector Builder

Change the segment length and arc radius. The construction works when arcs from both endpoints meet.

📐 Angle Bisector Lab

Choose an angle and see its bisector.

⬡ Regular Hexagon Maker

Six equilateral triangles make a regular hexagon.

🧩 Construction Rule Identifier

A line divides a segment into equal halves at 90°.

Worksheet Generator

Generate printable practice on perpendicular bisectors, 90° constructions, angle bisectors, copied angles, parallel lines, regular hexagons and tiling designs.



Real-Life Lab

Teacher Tools

Learning Outcomes

  • Construct perpendicular bisectors using equal arcs.
  • Construct a \(90^\circ\) angle at a point on a line.
  • Bisect an angle using compass arcs and congruent triangles.
  • Copy angles and use copied corresponding angles to construct parallel lines.
  • Construct \(60^\circ\), \(120^\circ\), and regular hexagons.
  • Connect constructions to arches, eyes, flowers, and tiling patterns.

Exit Ticket Prompts

  • Why does joining the two arc intersections give a perpendicular bisector?
  • How can a \(45^\circ\) angle be constructed from a \(90^\circ\) angle?
  • Why do six equilateral triangles fit around a point?