GR 9 3-5-6 LEARNERS
Page 1 of 2
NAME:
Gr 9
Date:
Time
1 hr.
CAPS
3-5 Construction of Geometric Figures Explore the minimum
Reference conditions for two triangles to be congruent
3-5-6 By construction, explore the minimum conditions for two
Topic
triangles to be congruent
Think First! [5 mins]
What is something that is unique?
The word unique comes from a word meaning one. Unique means “one of a kind”.
Constructing unique shapes means that however many times you try, with
certain sets of information you will only be able to create one sized shape.
If you draw a circle with a radius of 5 cm you will ALWAYS get the same sized
circle.
2.
Go ahead! [30 mins]
C
This activity is best done in groups of 4. If you are working on your own,
you will need to draw all 4 sets of triangles.
2.1
Each person in the group of 4 should accurately
construct one set of triangles on thin card or paper.
Write the triangle letter in the middle and any angle sizes
and side lengths neatly written inside the triangle.
2.2
5 cm
A 46°
7 cm
E
Cut out each triangle. Keep your sets of triangles in a box or envelope.
SET 1
A
B
C
D
E
F
G
Δ ABC with AB = 5 cm BC = 6 cm and CA = 4 cm.
̂ = 45°, L̂ = 65°, M
̂ = 70°
Δ KLM with K
Δ ABC with AB = 5 cm BC = 6 cm and 𝐵̂ = 70°
Δ ABC with BC = 9 cm, 𝐶̂ = 55° and BA = 8 cm
̂ = 74°.
Δ LMN with LM = 5,7 cm L̂ = 24° and N
̂
̂ = 80°.
Δ LMN with LM = 6,3 cm L = 32° and N
̂ = 90°
Δ PQR with PR = 5 cm QR = 3 cm and Q
SET 2
A
B
C
D
E
F
G
Δ PQR with PQ = 6 cm QR = 4 cm and RP = 5 cm
̂ = 70°, R
̂ = 65°, Q
̂ = 45°
Δ PQR with P
Δ PQR with PQ = 6 cm QR = 5 cm and 𝑄̂ = 70°
Δ PQR with PR = 8 cm, 𝑃̂ = 55° and RQ = 9 cm
̂ = 24° and Ĉ = 74°
Δ ABC with AC = 5,7 cm A
̂ = 32°
̂ = 68° and A
Δ ABC with AB = 6,3 cm B
̂ = 90°
Δ STU with ST = 5 cm UT = 3 cm U
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GR 9 3-5-6 LEARNERS
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SET 3
A
B
C
D
E
F
G
Δ KLM with KL = 4 cm LM = 5 cm and MK = 6 cm
̂ = 45° and K
̂ = 70°, G
̂ = 65°
Δ DGK with D
Δ KLM with KL = 5 cm LM = 6 cm and 𝐿̂ = 70°
̂ = 55°
Δ DCF with DC = 8 cm CF = 9 cm and 𝐷
̂ = 24° and Ẑ = 74°
Δ XYZ with YZ = 5,7 cm X
̂ = 32°
Δ XYZ with XY = 6,3 cm Ẑ = 80° and X
̂ = 90°
Δ DBC with BC = 5 cm BD = 3 cm and D
SET 4
A
B
C
D
E
F
G
Δ DGK with DG = 5 cm GK = 4 cm and KD = 6 cm
̂ = 65°, B
̂ = 45° and Ĉ = 70°
Δ ABC with A
̂ = 70°
Δ DGK with DG = 6 cm GK = 5 cm and G
Δ XYZ with XY = 9 cm, 𝑋̂ = 55° and YZ = 8 cm
̂ = 74°
Δ STR with ST = 5,7 cm Ŝ = 24° and R
̂ = 68° and U
̂ = 80°
Δ STU with ST = 6,3 cm T
̂ = 90°
Δ FGH with FG = 5 cm FH = 3 cm and H
3.
Check your work! (Work in groups of 4). [10 mins]
3.1
Check whether each set of triangles is the same.
Each group put together their sets of 4 triangles –
all the A triangles together;
all the B triangles together and so on.
3.2
Take each set of triangles and compare them by trying to stack them together.
You may have to turn some over or around, but keep trying until you are sure you
have explored all the possibilities.
4.
Think Again! (Work in groups of 4.) [15 mins]
4.1
Copy the table below and write down whether or not each set of triangles is unique
(exactly the same) or not unique (the triangles in each set are not necessarily the same)
For the unique triangles, say what information you were given.
Include information on the corresponding position of angles.
4.2
Δ Number
Unique
or not
SET A
SET B
SET C
SET D
SET E
SET F
SET G
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Information given
Some sets of facts give us unique
triangles. It does not matter how many
different times the information is used
to draw a triangle, the result will
always be the same shape. Triangles
that are exactly the same are known
as congruent triangles.
The sets of information that give us
congruent triangles are called the cases
for congruence.
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