Your learning journey
Select a valid triangle congruence criterion and use corresponding parts to build a short proof.
Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Congruent: same shape and size. Corresponding: matching position in the two figures. Included angle: between two specified sides. Hypotenuse: side opposite a right angle. Proof: a justified chain of statements.
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60°.
180° total.
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50°.
180−130.
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Opposite angles equal.
Use parallel sides.
Present
SSS fixes all three sides; SAS fixes two sides and their included angle; ASA fixes two angles and the side between them. RHS fixes a right angle, hypotenuse and another side. A rigid movement can then match the triangles. AAA fixes shape but permits different sizes. SSA is not a general congruence test.
Write vertices in corresponding order. List each equality with its given reason, name the criterion, then deduce equal matching parts. A shared side equals itself; a picture is not proof.
Optional scaffold
Pair sides by length.
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SSS.
All three corresponding sides match.
Optional scaffold
Check included position.
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SAS.
The angle lies between the equal sides.
Optional scaffold
Identify the side joining the two angles.
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ASA.
Two corresponding angles and included side match.
Optional scaffold
Distinguish hypotenuse from another side.
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RHS.
Both right angles must be given.
Apply
Optional scaffold
Mark what is known.
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SSS; SAS; RHS.
Each specifies enough corresponding information.
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AB=CD and BC=DA, opposite sides of a parallelogram; AC shared; SSS.
Correspondence A↔C, B↔D, C↔A.
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AB=AD, BC=DC, AC shared; ABC and ADC congruent by SSS, so matching angles BAC and CAD are equal.
Conclude only after proving congruence.
No calculator is needed. Length totals can be checked, but congruence requires reasons, not numerical output.
Apply and extend
Intentional practice feedback after your attempt
Both have 60° angles but different sizes; AAA does not prove congruence.
Equality of angles gives similarity.
Intentional practice feedback after your attempt
Drawings may be inaccurate. Use the three stated/shared equal side pairs and SSS.
Give evidence independent of appearance.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
A perpendicular bisector is the set of points equally distant from two fixed points. Equal-radius compass arcs from the endpoints identify two such points; joining them creates the line.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
SSS: all three corresponding sides equal.
Deep challenge
Reveal a worked check after attempting
No. SSA is generally insufficient; more than one triangle may fit.