PL BM P5L40 Quadrilaterals WS

Primary 5: Boost! Math

Primary 5

Boost! Math

Name Quadrilaterals (Lesson 40)
Tutor Quadrilaterals (Lesson 40)
Topic

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Primary 5: Boost! Math

Quadrilaterals

Parallelogram B ABCD is a parallelogram.
q Opposite sides are parallel.
A AB = DC; AD = BC (opposite sides are equal)
p r ∠p = ∠r ; ∠q = ∠s
s C
∠p + ∠s = 180° ; ∠q + ∠r = 180°
D ∠p + ∠q = 180° ; ∠s + ∠r = 180°
∠p + ∠q + ∠r + ∠s = 360°

Rhombus

A B ABCD is a rhombus.
p q Opposite sides are parallel.
AB = DC = AD = BC (4 sides are equal)
s r ∠p=∠r ;∠q=∠s
D C
∠ p + ∠ s = 180° ; ∠ q + ∠ r = 180°
∠ p + ∠ q = 180° ; ∠ s + ∠ r = 180°
∠ p + ∠ q + ∠ r + ∠ s = 360°

Trapezium

A B ABCD is a trapezium.
p q Only one pair of parallel sides,AB // DC.

s r ∠ p + ∠ s = 180° ; ∠ q + ∠ r = 180°
D C
∠ p + ∠ q + ∠ r + ∠ s = 360°

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Primary 5: Boost! Math

The following quadrilaterals are not drawn to scale, find the unknown angles
without using calculators.
1. Find the unknown marked angles in the following parallelograms.

(a)
78°

f

Ans: ∠ f =

(b) 101°
f
g

Ans: ∠ f =
∠g=

(c) 68°
g f

Ans: ∠ f =
∠g=

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Primary 5: Boost! Math

2. Find the unknown marked angles in the following rhombuses.
(a)
36°
f

Ans: ∠ f =

(b)
132°

f
g 23°

Ans: ∠ f =
∠g=

(c)
24° f

g

Ans: ∠ f =
∠g=

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Primary 5: Boost! Math

3. Find the unknown marked angles in the following trapeziums.
(a)
122°
g

64° f

Ans: ∠ f =
∠g=

(b) g
46° 75°

f

104°

Ans: ∠ f =
∠g=

(c) g
74° 236°

f

Ans: ∠ f =
∠g=

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Primary 5: Boost! Math

4. In the figure below, QRS is an equilateral triangle and PQST is a rhombus.
∠ PRS = 34°. Find ∠ PTS.
PQ

34° R
TS

Ans:

5. In the figure, PQRS is a trapezium. PSU and TSR are straight lines.
∠ TSU = 86°. ∠ PQR is twice ∠ QRS.

(a) Find ∠ SPQ. Q
(b) Find ∠ PQR.

P

T R
S

86°

U

Ans: (a)
(b)

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Primary 5: Boost! Math

6. In the figure below, PQRS is a rhombus. STQ is a straight line and SP = ST.
∠PST is 24° less than ∠STP. Find ∠SRQ.

S

P

T
R

Q

Ans:

7. In the figure below, ABCD is a rectangle and all the sides of BEFG are equal.

∠BGF is 2 of ∠GBE.
7

(a) Find ∠GBF.
(b) Find ∠DHB.

AB

DH E
G

F

C

Ans: (a)
(b)

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Primary 5: Boost! Math

8. In the figure,ABCD is a rhombus and BDFE is a parallelogram.
∠BAD = 58°. ∠GBC = 16° and ∠GDE = 33°.

(a) Find ∠DBG.
(b) Find ∠FDE.

A B
58° 16°

D 33° G C
E

F

Ans: (a)
(b)

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Primary 5: Boost! Math

9. In the figure, a rectangular piece of paper is folded along GE and EC as shown..
∠FGE = 62° and ∠DCE = 53° Find ∠FED.

A B
F D

G 62° 53° C

E

Ans:

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Primary 5: Boost! Math

10. In the figure, PQRS and TUVW are overlapping trapeziums.
AB and QXR are straight lines.
YW is parallel to QX. ∠APS = 48°. ∠UQX = 138° and ∠QUV = 56°.

(a) Find ∠QYW.
(b) Find ∠UVX.

AP TU B
48° 56° V

S YQ
138°

WX

R

Ans: (a)
(b)

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Primary 5: Boost! Math

11. In the figure, PQRS is a trapezium, PQT is an equilateral triangle and SVU is a
right-angled triangle. SRU is a straight line. SR = RU = RV.
∠SPT = 41°. ∠QRU = 108° and ∠RVU = 26°.

(a) Find ∠PSR.
(b) Find ∠QRV.

P Q
41°

ST 108° U
R

26°
V

Ans: (a)
(b)

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