Congruent triangles
Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent
Lesson
Set out your lesson
“Congruent triangles means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape or angle name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Congruent triangles, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Congruent triangles, not mastery.
Share and support
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Teaching approaches
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1 approach
Congruent triangles means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper shapes or a ruler and pencil; Shape or angle name cards. 1. Say the goal of Congruent triangles in plain words once. 2. Adult traces or shows one shape/angle and names a key property. 3. Child measures or classifies three shapes/angles and names a property each time. 4. Fresh check: one fresh property name. Record and stop. Done: three correct property names with a sketch or measure. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceCongruent triangles practice
Practice key ideas from Congruent triangles.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Congruent triangles. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- State which congruence criterion (SSS, SAS, ASA, or RHS) applies to a given pair of triangles
- Use the notation △ABC ≅ △DEF and match corresponding sides and angles
- Use two non-congruent triangles that share two sides and a non-included angle to explain why SSA is not a congruence criterion
“If your child is shown two triangles where all three sides of one match all three sides of the other, can they explain why those triangles must be identical in shape and size?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 12–14
Standards