Euclidean Geometry Riders: Proving It, With Reasons (Grade 10)

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Grade 10 · Euclidean Geometry

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Mark

/ 30

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

1
Write down the reason you would quote for the statement “x = 65°” if the two angles are on opposite sides of a transversal, between two parallel lines AB and CD.
(2)
2
Why is a correct angle written with no reason usually worth only half the marks?
(2)
3
In △PQR, ST ∥ QR with S on PQ and T on PR. P̂ = 44° and Q̂ = 76°. Determine, with reasons, the size of PŜT.
(3)
4
Using the same triangle, determine, with a reason, the size of R̂.
(3)
5
List the FOUR conditions for congruency and state which one applies only to right-angled triangles.
(4)
6
ABCD is a parallelogram with diagonal BD drawn. Prove that △ABD ≡ △CDB.
(4)
7
State THREE different ways of proving that a quadrilateral is a parallelogram.
(3)
8
In △ABC, D and E are the midpoints of AB and AC. If DE = 7,5 cm and AĈB = 58°, determine BC and AÊD, with reasons.
(4)
9
Explain why you may NOT use the reason “opp sides of a parm” inside a proof whose conclusion is that the shape is a parallelogram.
(2)
10
PQRS is a quadrilateral with PQ ∥ SR and PQ = SR. Prove that PQRS is a parallelogram.
(3)

TOTAL: 30 marks