Reach for the Star

Pythagoras in two dimensions · Optional extension

L038 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

A rectangle is 9 cm by 12 cm. Find its diagonal and the perimeter of one of the right triangles formed by that diagonal.

Reveal a worked check after attempting

Diagonal=15 cm; triangle perimeter=9+12+15=36 cm.

Deep challenge

A triangle has sides 8, 15 and 17 cm. Prove it is right-angled and find its area.

Reveal a worked check after attempting

8²+15²=17²; area=8×15/2=60 cm².

Recall & Review: feedback and extension integration

Lesson L038: Pythagoras in two dimensions

Objective: Use Pythagoras to find a missing length in a right-angled triangle.

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: A rectangle is 9 cm by 12 cm. Find its diagonal and the perimeter of one of the right triangles formed by that diagonal.

Deep challenge: A triangle has sides 8, 15 and 17 cm. Prove it is right-angled and find its area.