Solutions for Similarity Practice

1)

Use the facts given in the diagram to find the ratio of:

 a) 1 : 1 b) 1 : 3 c) 1 : 3 d) 1 : 3 e) 1 : 2 f) 1 : 2

2)

a)x = 3/2
b) Using the mid point theorem, x = 2 and y = 3.
c), 3x = 32, so x = 32/3.

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3) In the two diagrams shown here, . Find the value for x in both cases.

a) t 7x = 28, so x = 4.

b) t 7x = 42, so x = 6.

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4) The sides AB and AC in ÊABC are divided at X and Y respectively in the ratio of 3:2. Find the ratio of ÊABC to ÊAXY.

ÊABC Ã ÊAXY since and ÉA is common.

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5) Since we know that k2 = , then we know that k = .

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6)

Given: ABCD is a trapezoid with AByCD.

The diagonals AC and BD intersect at O.

Req'd to Prove: ÊOAB Ã ÊOCD.

Proof: In Ês OAB and OCD:

ÉOAB = ÉOCD (alternate És)

ÉAOB = ÉCOD (opposite És)

ÉABO = ÉODC (Ê angle sum thm.)

ÊOAB Ã ÊOCD (AAA)

Side Ratios:

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7) Solution:

ÉQ = 90) = ÉS and ÉPRQ = ÉTRS (opposite angles)

ÊPQR Ã ÊTRS (AAA)

(proportional sides)

3.2x = (4.5)(9.6) u x = 13.5

The river is 13.5 meters wide.

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8) Solution: Since the triangles ABE and DCE are similar, and AB : DC = BE : CE

u AB = meters.

In this question, it is easy to find that the tree is 3 meters high
since the ratio of BE : CE = 2 : 1.
Therefore the tree must be twice as tall as Harry.

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