|Solutions for Similarity Practice|
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|
a)x = 3/2
b) Using the mid point theorem, x = 2 and y = 3.
c), 3x = 32, so x = 32/3.
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.
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.
5) Since we know that k2 = , then we know that k = .
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)
ÉQ = 90) = ÉS and ÉPRQ = ÉTRS (opposite angles)
ÊPQR Ã ÊTRS (AAA)
3.2x = (4.5)(9.6) u x = 13.5
The river is 13.5 meters wide.
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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