Question

example 3
$overline{vr}$, $overline{vz}$, and $overline{zr}$ are midsegments of $\triangle uwy$. find the value of $x$.
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example 4

1. maps in mikas town, cay street and bay street are parallel. find the value of $x$, the distance from cay street to bay street along earl street.

Explanation:

Step1: Solve Q5 (Midsegment Length Rule)

A midsegment is half the length of the side it is parallel to, so $x = 2 \times 25$

Step2: Solve Q6 (Midsegment Parallel Angle Rule)

Midsegments create congruent corresponding angles, so $x = 57$

Step3: Solve Q7 (Midsegment Length Rule)

A midsegment is half the length of the side it is parallel to, so $x = \frac{2.7}{2}$

Step4: Solve Q8 (Triangle Angle Sum Rule)

First find the third angle in $\triangle YZR$: $180 - 44 - 76 = 60$. Midsegments create congruent corresponding angles, so $x = 60$

Step5: Solve Q9 (Proportional Segments Rule)

Set up a proportion for parallel lines: $\frac{x}{1.4} = \frac{0.8}{1+0.8}$, so $x = 1.4 \times \frac{0.8}{1.8}$

Answer:

1. $50$
2. $57^\circ$
3. $1.35$
4. $60^\circ$
5. $\frac{28}{45} \approx 0.62$ km