Triangle Building – Starter Exercise
With the information provided in each question, attempt to draw a triangle using a pencil, protractor and ruler
where this is the only triangle that can be made. If there is no unique answer (you need more information), give the reason why.
1.
Draw the triangle with two lengths, 3cm and 4cm with a 60 o angle between them.
2.
Draw the triangle with two angles that are 50 o on either end of a 4cm length.
3.
Draw the triangle with two lengths 3.5cm and 4cm with an angle of 70 o touching just one of the lengths.
4.
Draw the triangle with a length of 5cm between an angle of 30 o and 40 o .
5.
Draw the triangle with angles 40 o , 90 o and 50 o .
6.
Draw a triangle with lengths 3cm, 4cm and 5cm.

Congruence – When two shapes are exactly the same shape and size, they are congruent.
Two triangles are congruent when any of the following are true.
 Every pair of corresponding sides for each triangle is the same in length. (SSS)
3 cm
B
2cm
≅
3 cm
Y
2cm
∆ ABC ≅ ∆ XYZ
A
A C
X
Z
4cm 4cm

Two pairs of corresponding sides for each triangle are the same in length and the each of the angles between them are the same size. (SAS)
B Y
3 cm
105 o
2cm
C
≅
X
3 cm
105 o
2cm
Z
∆ ABC ≅ ∆ XYZ
A
A
A
 Two corresponding pairs of angles for each triangle are the same size and any corresponding pair of sides are the same length. (AAcorS)
B
3 cm 105 o ≅ 3 cm
30 o
C X 30 o
Y
105 o
Z
∆ ABC ≅ ∆ XYZ
30 o
B
105 o
B
105 o
30 o
4cm
2cm
C
C
≅
≅
X
X
30 o
Y
105 o
2cm
Z
Y
105 o
30 o
4cm
Z
∆ ABC ≅ ∆ XYZ
∆ ABC ≅ ∆ XYZ

In particular for right-angled triangles, the hypotenuses and another corresponding pair of sides are the same length. (RHS)
C Z
5cm ≅ 5cm
∆ ABC ≅ ∆ XYZ
A
3 cm
B X
3 cm
Y

Applying the Tests for Congruence
Please answer the questions below.
1.
Look at the two triangles.
10cm
8cm 𝑥 𝑦
7cm 7cm a.
The two triangles are congruent. Find 𝑥 and 𝑦 . 𝑥 = ________ 𝑦 = ________ b.
Please circle the correct test for congruence for these triangles assuming that we are also given lengths 𝑥 and 𝑦 .
SAS ASA SSS AAcorS
2.
State whether the altered triangle is congruent to its original by stating “Yes” or “No”. a.
A triangle repositioned and turned 90 o . b.
A triangle doubled in size. c.
A triangle reflected across its base. d.
A triangle with one angle altered to be double its original size. e.
A right-angled triangle repositioned and redrawn with two pairs of corresponding edges the same length.
3.
Explain whether the triangles below are congruent or not.
8cm
B
75
A o
13cm
C
8cm
X
75
Y o
13cm
Z
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
4.
Please look at the triangles below.
A
Y
8cm 𝑦 𝑦 o
10cm
B
10cm
8cm C X a. Show that the triangles are congruent.
Z
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________ b. Find angles 𝑥 and 𝑦 . 𝑥 = ________ 𝑦 = ________
5.
Explain why the two triangles below are not congruent.
B
30 o
55
A o
8cm
C
X
Y
55 o
8cm
30 o
Z
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___________________________________
___________________________________
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