How to find if two triangles are similar - ISEE Upper Level (grades 9-12) Quantitative Reasoning

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Question

$\Delta ABC \sim \Delta DEF$

Which is the greater quantity?

(a)

(b)

Answer

$\Delta ABC \sim \Delta DEF$ , so by definition, the sides are in proportion. Therefore,

$\frac{DE}{AB} = \frac{EF}{BC}$ .

Substitute:

$\frac{DE}{18} = \frac{EF}{17}$

$\frac{DE}{18} \cdot 18 = \frac{EF}{17}\cdot 18$

$DE = \frac{18}{17}\cdot EF$

, so (a) is greater.

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Question

$\Delta ABC \sim \Delta DEF$

Which is the greater quantity?

(a)

(b)

Answer

$\Delta ABC \sim \Delta DEF$ , so by definition, the sides are in proportion.

(a) $\frac{BC}{EF} = \frac{AC} {DF}$

Substitute and solve for :

$\frac{BC}{27} = \frac{16} {24}$

$\frac{BC}{27} \cdot 27 = \frac{16} {24} \cdot 27$

(b) $\frac{DE}{AB} = \frac{DF}{AC}$

Substitute and solve for :

$\frac{DE}{12} = \frac{24}{16}$

$\frac{DE}{12} \cdot 12= \frac{24}{16}\cdot 12$

The two are equal.

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