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Pythagoras in two dimensions

L038 · GCSE Mathematics 1MA1 · 60 minutes

Objective: Use Pythagoras’ theorem to find a missing length in a right-angled triangle and justify whether a triangle is right-angled.

Connect & Check · 5 min

Baseline

Which side is the hypotenuse in a right-angled triangle?

Calculate 9², 12² and √225.

Share · 5 min

Route choice

Present · 12 min

A rectangle measures 9 cm by 12 cm. Find its diagonal.

Apply · 25 min

Supported → independent

Find the hypotenuse of a right triangle with legs 6 cm and 8 cm.

A ladder reaches 6 m up a wall and its foot is 2.5 m from the wall. Find the ladder length.

A rectangular field is 30 m by 40 m. Find the straight-line distance between opposite corners.

Recall & Review · 8 min

A right triangle has hypotenuse 10 cm and one shorter side 6 cm. Find the other side and show a check.

Points and self-check

Complete every stage to unlock.

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.