Mathable Logo

Mathable Smart Lab

TRACK 2 • GEOMETRYStrand: Triangle Construction and Reasoning

A Tale of Three Intersecting Lines Smart Lab

Construct triangles, test triangle inequality, explore angle-sum property, classify triangles, and reason about altitudes.

What is this chapter about?

A triangle is a closed figure made by three line segments joining three vertices. This chapter turns triangle construction into reasoning: when can a triangle be made, and what angle facts are always true?

Constructing from sides: Draw a base, then use compass arcs from both endpoints. The intersection of arcs gives the third vertex.
Triangle inequality: A triangle exists only when each side is smaller than the sum of the other two sides.
Angle sum: The three angles of a triangle always add up to \(180^\circ\).

Change the side lengths and watch whether the construction arcs intersect.

Rules Hub

Triangle Inequality

\(a+b>c,\ b+c>a,\ c+a>b\)

Quick test: the two smaller sides must add to more than the longest side.

Equilateral Triangle

All three sides are equal.

Isosceles Triangle

Two sides are equal.

Scalene Triangle

All three side lengths are different.

Angle Sum Property

\(\angle A+\angle B+\angle C=180^\circ\)

Altitude

A perpendicular line segment from a vertex to the opposite side.

Guided Solve Lab

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


Activity Zone

🎛️ Triangle Inequality Tester

Enter three side lengths. The lab checks if a triangle exists and shows a construction-style diagram.

🧭 Construct a Triangle from Three Sides

Use compass arcs mentally: base = longest side, radii = other two sides.

🔺 Angle Sum Lab

Pick two angles. The lab decides if a triangle is possible and finds the third angle.

Angle A
°
Angle B
°
Angle C
60°

🧩 Triangle Classifier

Classify a triangle by side lengths.

Sides: 4, 4, 6

Worksheet Generator

Generate printable practice on triangle construction, triangle inequality, angle sum, and classification.



Real-Life Lab

Teacher Tools

Learning Outcomes

  • Construct an equilateral triangle using compass arcs.
  • Construct a triangle when three sides are given.
  • Use triangle inequality to decide if a triangle can exist.
  • Construct triangles from two sides and the included angle, or two angles and the included side.
  • Use the angle sum property to find missing angles.
  • Classify triangles as equilateral, isosceles, scalene, acute, right, or obtuse.
  • Identify and construct altitudes of triangles.

Exit Ticket Prompts

  • Can sides 3 cm, 4 cm, and 8 cm form a triangle? Explain without constructing.
  • If two angles of a triangle are 50° and 70°, what is the third angle?
  • How does a compass help construct a triangle with sides 4 cm, 5 cm, and 6 cm?