AC9M10SP01Year 10SpacePractised on site

AC9M10SP01 — Year 10 Space

Official Curriculum Content Description:

apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems

Worked Examples (1)

Example 1Circle Geometry Theorems
M,N,K,LM, N, K, L are four points in order on the circumference of a circle, forming a cyclic quadrilateral MNKLMNKL. If angle ∠MNK=96∘\angle MNK = 96^\circ, find the size of opposite angle ∠MLK\angle MLK in degrees.
Common mistake: Assuming opposite angles in a cyclic quadrilateral are equal.
Correct Answer:84°84°
Accepted: A unit is optional (degrees, deg, ° all accepted).
Worked Solution:
1. Opposite angles in a cyclic quadrilateral sum to 180∘180^\circ: ∠MLK=180∘−96∘=84∘\angle MLK = 180^\circ - 96^\circ = 84^\circ.

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