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 **Ê****ABC** are divided at **X** and **Y** respectively in the ratio of 3:2. Find the ratio of **Ê****ABC** to **Ê****AXY**.

ÊABC **Ã**** **ÊAXY since and ÉA is common.

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5) Since we know that **k ^{2} =** , then we know that

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6)

**Given:** ABCD is a trapezoid with AByCD.

The diagonals AC and BD intersect at O.

**Req'd to Prove:** **Ê**OAB** ****Ã**** ****Ê**OCD.

**Proof:** In **Ê**s OAB and OCD:

ÉOAB = ÉOCD (alternate És)

ÉAOB = ÉCOD (opposite És)

‹ ÉABO = ÉODC (Ê angle sum thm.)

‹ **Ê**OAB** ****Ã**** ****Ê**OCD (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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