Reach for the Star

Congruence and geometric reasoning · Optional extension

L027 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

State a valid congruence test for sides 5,7,8 cm in two triangles and explain.

Reveal a worked check after attempting

SSS: all three corresponding sides equal.

Deep challenge

Two triangles have equal side lengths 5 and 7 cm and a non-included equal angle. Must they be congruent?

Reveal a worked check after attempting

No. SSA is generally insufficient; more than one triangle may fit.

Recall & Review: feedback and extension integration

Lesson L027: Congruence and geometric reasoning

Objective: Select a valid triangle congruence criterion and use corresponding parts to build a short proof.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: State a valid congruence test for sides 5,7,8 cm in two triangles and explain.

Deep challenge: Two triangles have equal side lengths 5 and 7 cm and a non-included equal angle. Must they be congruent?