In pyramid P–ABC, PC⊥plane ABC, PC=3, ∠BCA=π/2. D lies on AB and E on BC; CD=DE=√2, CE=2 and EB=1. Prove ∠CDE=π/2.

01 / Standard#Your turn

Official paper · jm02-2022 · 1(b)(i) · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The side opposite angle D is CE.

Hint 2

Use the converse of Pythagoras.

Worked solution

∠CDE=π/2.

Checks and common pitfalls: The longest side CE is the hypotenuse.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Compare the squared lengths.
$CD^2+DE^2=2+2=4=CE^2$
Therefore triangle CDE is right at D.
$\angle CDE=\pi/2$

Think first. Reveal a hint when the class is ready.

2022 JM02