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Mathable Smart Lab

TRACK 2 • GEOMETRY Strand: Congruence and Triangle Reasoning

Geometric Twins Smart Lab

Explore congruent figures, triangle congruence conditions, corresponding parts, and properties of isosceles and equilateral triangles.

What are Geometric Twins?

Congruent figures are exact copies: they have the same shape and size. They can be moved, rotated, or flipped and still fit exactly over each other.

Congruent figures: Same shape and same size; one can be superimposed exactly on the other.
Triangles: Measuring all three sides is enough to recreate a congruent triangle. This is the SSS condition.
Careful: Same three angles gives the same shape, but not necessarily the same size, so it does not guarantee congruence.

Adjust the angle. The two arms can have same lengths but form non-congruent shapes when the included angle changes.

Rules Hub

SSS

Side–Side–Side

If all three corresponding sides are equal, triangles are congruent.

SAS

Side–Angle–Side

If two sides and the included angle are equal, triangles are congruent.

ASA

Angle–Side–Angle

If two angles and the included side are equal, triangles are congruent.

AAS

Angle–Angle–Side

If two angles and a corresponding non-included side are equal, triangles are congruent.

RHS

Right angle–Hypotenuse–Side

For right triangles, RHS guarantees congruence.

Not enough

AAA and SSA do not always guarantee congruence.

Guided Solve Lab

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


Activity Zone

🎛️ Congruence Tester

Choose the information given for two triangles. The lab tells whether congruence is guaranteed.

🔁 Correspondence Matcher

If \(\triangle ABC \cong \triangle XYZ\), identify matching parts.

A ↔
B ↔
C ↔

📐 Isosceles Angle Lab

In an isosceles triangle, angles opposite equal sides are equal.

🧩 Rule Identifier

Three corresponding sides are equal.

Worksheet Generator

Generate printable practice on congruent figures, congruence conditions, corresponding vertices, and isosceles/equilateral triangle properties.



Real-Life Lab

Teacher Tools

Learning Outcomes

  • Explain congruent figures as exact copies.
  • Identify corresponding vertices, sides, and angles.
  • Apply SSS, SAS, ASA, AAS, and RHS congruence conditions.
  • Recognise why AAA and SSA do not always guarantee congruence.
  • Use congruence to reason about isosceles and equilateral triangles.

Exit Ticket Prompts

  • Why do three equal angles not guarantee congruence?
  • State the SAS condition.
  • If \(\triangle AIR \cong \triangle FLY\), which angle corresponds to \(\angle I\)?