Question

geometry 452/451 c w hw solving proportions 2-4-26 name1) complete each proportion.a) $\frac{gn}{gh}=\frac{gm}{?}$b) $\frac{nm}{hj}=\frac{?}{gj}$c) $\frac{?}{mn}=\frac{gh}{gn}$d) $\frac{gj}{?}=\frac{gh}{gn}$2) find the value of x. write and solve a proportion. show work.a)b)c)d)

Explanation:

Part 1: Complete each proportion

Step1: Apply Triangle Proportionality Theorem

Since $MN \parallel HJ$, corresponding segments are proportional.

Step2: Match corresponding sides

A) $\frac{GN}{GH} = \frac{GM}{GJ}$
B) $\frac{NM}{HJ} = \frac{GN}{GI}$
C) $\frac{GJ}{MN} = \frac{GH}{GN}$
D) $\frac{GJ}{GM} = \frac{GH}{GN}$

Step1: Set up proportional sides

$\frac{x}{8} = \frac{5}{5+6}$

Step2: Simplify denominator

$\frac{x}{8} = \frac{5}{11}$

Step3: Solve for $x$

$x = 8 \times \frac{5}{11}$

Step1: Set up proportional sides

$\frac{x}{8} = \frac{20}{20+8}$

Step2: Simplify denominator

$\frac{x}{8} = \frac{20}{28} = \frac{5}{7}$

Step3: Solve for $x$

$x = 8 \times \frac{5}{7}$

Answer:

A) $GJ$
B) $GN$
C) $GJ$
D) $GM$

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Part 2: Find the value of $x$

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2A