Key Stage 3
Measures, Shape and Space Dimension
Learning Unit: Quadrilaterals
Learning Objectives:
· extend the idea of deductive reasoning in handling geometric
problems involving quadrilaterals
· deduce the properties of various types of quadrilaterals but
with focus on parallelograms and special quadrilaterals
Programme Title: Quadrilaterals
Programme Objectives
1. Recognize the definitions and properties of various types of quadrilaterals
including a trapezium, a parallelogram, a rectangle, a square, a rhombus and
a kite.
2. Explore the relations between the sides, the interior angles and the diagonals
of parallelograms and special quadrilaterals.
3. Extend the idea of deductive reasoning to identify the properties and handle
related geometric problems involving quadrilaterals.
Programme Content
The story is about a competition on designing an ideal country club for Hong
Kong. A student wants to use various quadrilaterals as the shapes of the
buildings in his design. In the process, he has to make it clear the definitions
and properties of various types of special quadrilaterals. It also revealed that we
can easily observe and appreciate the beauties of various quadrilaterals in the
surroundings around us.
The programme starts with a quadrilateral with a pair of parallel opposite sides
to introduce the definition and properties of a trapezium. Then, there comes a
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quadrilateral with two pairs of opposite sides, a parallelogram. The various
properties of a parallelogram: opposite sides equal, opposite angles equal,
diagonals bisect each other, are explored. Deductive reasoning, instead of
intuitive approach is employed in the investigation process.
The relation between a rectangle, a rhombus and a square is introduced and
their properties are elaborated. In addition, the programme also comes across
the introduction of a kite. It emphasizes that a kite is not a parallelogram.
Examples on solving geometric problems involving quadrilaterals are provided.
To further consolidate the recognition of the definitions of various
quadrilaterals, the last part of the programme illustrates that the properties of a
quadrilateral, on the converse, can be used as tools to identify its special type.
Worksheet Answers
1.
a = 400, x = 3, y = 5.
2.
∠ ABE = 800
3.
Proofs are omitted.
4.
Proofs are omitted.
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Key Stage 3 ETV Programme《Quadrilaterals》
Worksheet
Review some problems discussed in the programme.
1. ABCD is a parallelogram.
∠ DAC = 2a+100 , ∠ CAB = 500 ,
∠ BCD = 1400 , AD = (5x-6) cm,
BC = 9 cm, OA = (2x+y) cm,
OC = (3x+2) cm.
Find the values of a, x and y.
2. BCDE is a rhombus and
∠ DEC = 400 .
Find the value of ∠ ABE.
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3. ABCD is a kite.
DA = DC, BA = BC.
(i) Prove that ∠ BDA = ∠ BDC.
(ii) Prove that △ADE ≅ △CDE.
(iii) Prove that AC ⊥ DB.
4. In the quadrilateral PQRS, the
diagonals are perpendicular
bisectors of each other, that is
PR ⊥ SQ and
PO = QO = RO = SO.
(i) Prove that:
PQ = QR = RS = SP.
(ii) Prove that PQRS is a square.
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