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• Constructing triangles • • • • •••••••••• 45
+·This is one way to construct
a triangle with sides of • Draw a freehand sketch of triangle 7 • Draw a freehand sketch of triangle DEF in which the base DE
3cm, 4 cm and 5cm ABC in which AB; 6cm, AC;5·5cm is Bern long, LEDF; 42° and LFED; 57'.
and BC ; 4·8 cm. onglaDFE
• Construct triangle DEF accurately.
Rule o line the • Measure the missing measurements length OF
length of • Mork the vertices ABC and the and record them in a table.
one side length of the sides. lengthEF
,A .. !!! • Drow a freehand sketch and then construct triangle XYZ
Set the compasses in which XZ is 7·8 cm long, LYXZ; 85' and LXZY; 32' .
~
to the length ~
of another side • Measure and record the missing measurements.
A bcM 8 • Triangle JKL hos side JK 6·4 cm long, ~
L LJK; 75° and side JL 5·2 cm long. -"'t ,
[g3 Adopt the instructions in the box • Draw a freehand sketch first and then .,.·<:, <~ ' f ,.! /.~-~='*>
1
Drow on ore
like this. to construct the triangle ABC.
@] Measure the angles and record . ;:~:~~~~~~· i~::,:~\}
in a table.
angle stze lndegrees
• Draw a sketc~ of, ~nd then construct, !'>ol ~
LB triangle UVW 1n which UV; 6·2 cm, ~
Set the compossestl L WUV ; 48' and UW ; 6·2 cm. , ·
~~ :~: !~~r~t:ide. 1 ~
I@ Check that the total of the angles o W"<";°'o'"'°'''' ;,,,W,
is 180'.
t_i__!_~_ +
~ Construct another triangle KLM
in which KL; 7·5cm, KM; 8·8cm
Drow o second
ore l!ke this, , and LM; 4·3cm.
Draw a freehand sketch first.
crossing~
rEJ Measure and record the angles
OS in@J r CHALLENGE
... A' Check the total of the angles. Several people are asked to construct triangle PQR,
Comp~ete the triangle where PO; 6cm, PR; Scm and LR; 55' .
likethrs. ~ CHALLENGE
• Why is it not possible to construct • Find some of the triangles they might construct.
Check the length of the a triangle with sides Bern, 4cm • Which measurement should be altered to make sure
triangle's sides. and 3 cm long? that all the triangles are congruent?
B
Practical: constructing triangle ABC, using given lengths of sides. Practical: constructing triangle DEF, using given measurements.
Angle DFE = 81 °; Length DF = 6· 7 cm ; Length EF = 5·4 cm .
LA = 4qo, L 8 = 60°, LC = 71 °
Practical: constructing triangle XYZ, using given measurements.
Angle XYZ = 63°; Length YZ = 8· 7 cm ; Length XV = 4·6 cm .
Practical: check that the angle sum Practical: constructing triangle
is 180°. KLM, using given lengths of sides.
Practical: constructing triangle JKL, using given measurements.
Angle JKL = 45°; Angle JLK = 60°; Length LK = 7· 1 cm .
Challenge
Challenge Practical: constructing triangle Different triangles can be
UVW, using given measurements. constructed from the given data.
The sum of the lengths of the two shorter sides is less than the length of
the longest side. Triangle UVW is an isosceles If angle P is 55°, instead of angle R,
triangle. all the triangles will be congruent.
