Scale Factor
Similar triangle
Trigo ratio
Pythagoras’ Theorem
100
△PRQ is similar to △ACB. Calculate the scale factor.
scale factor = 3
100
What is definition of similar triangles?
Triangles that have the same shape, different size.
Or similar triangles are enlargements or reductions of each other
Or two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
100
What are the three trigonometry ratios? Express these three ratios between the different pairs of sides.
Sin(θ) = O/H
Cos(θ)= A/H
Tan(θ)= O/A
100
What is the formula of Pythagoras’ Theorem?
c2 = a2 + b2
200
What is the ratio of line AB to line PQ? Simply your answer.
3:1
200
Identify which two are similar. Also, identify the similarity test that the pair satisfy.
A and D are similar, because the pair satisfy RHS.
200
Find the value of f correct to two decimal places.
f ≈ 5.46
200
Use Pythagoras’ Theorem to find the unknown side length in the triangles below.
x = 24m
300
△EDC is similar to △NML. Find the unknown side of x and y.
x = 42
y = 20
300
Determine the scale factor between the following two circles:
4
300
Sally measures the angle of elevation to the top of a tree from a point 20 m away to be 43°. Find the height of the tree h, to the nearest whole number.
h = 18 m
300
The screen on a handheld device has dimensions 9 cm by 5 cm, and a diagonal of length x cm. Find the value of x, correct to two decimal places.
x = 10.30cm
400
Jenny wants to find the height of her school's flag pole. During recess, she measures the length of the flag pole's shadow to be 335 cm. Her friend then measures her own shadow, which turns out to be 95 cm.
The triangles formed by casting these shadows are similar.
If Jenny is 160 cm tall, what is the height of the flag pole? Round your answer to the nearest whole centimetre.
h = 564 cm
400
a) Identify two similar triangles.
b) Given that KL=20, what is the length of MN?
a) △JNM ~ △JLK. ∵ AAA
b) MN = 5
400
Use sin to show that the two triangles below are similar by the similarity test AAA. Explain your answer with a sentence.
In △PRQ, sin(Q) = 4/7 = 0.571
In △ACB, sin(B) = 12/21 = 0.571
This shows that angles Q and B are the same. Therefore, the triangles are similar by the rule AAA.
400
Two flag posts of height 12m and 17m are erected 20m apart. Find l, the length of the string needed to join the tops of the two posts, correct to one decimal place.
l = 20.6m
500
What is the scale factor from △ABC to △A′B′C′?
2
500
Are △ABC and △ADE similar? If it is similar, Explain how you know that the following triangles are similar by writing a similarity statement, including the appropriate similarity test.
First, △ABC and △ADE have a common angle at ∠A.
Second, DE and BC are parallel, so ∠ADE=∠ABC since they are alternate angles on parallel lines.
Similarly, ∠AED=∠ACB.
Therefore, △ABC ~ △ADE. ∵AAA
500
Find the value of x, the side length of the parallelogram, to the nearest centimetre.
x = 34 cm
500
Marge's house has the outer dimensions as shown in the diagram below, find the height of the house, h, correct to one decimal place.
h = 5.2m