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In the diagram $\triangle{MNP}$ with $R$ on $MP$ and $T$ on $MN$ is given such that $RT \parallel PN$. S is a point on $PN$ such that $TS \parallel MP$.

MR = 10 units

RP = 4 units

MT = 8 units

RT = 9 units

TN = x units

SN = y units 1. Calculate, stating reasons, the numerical value of $x$
2. What type of quadrilateral is $RTSP$? Give a reason for the answer.
3. Hence calculate, stating reasons, the numerical value if $y$
4. Hence, show with calculations, that $\triangle{MRT} ||| \triangle{TSN}$

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## 1 Answer

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1. x/8 = 4/10 , proportion of triangle sides when divided by parallel line

10x = 32

x = 3.2

2. It is a parallelogram as both pairs of opposite sides are parallel.

3. y/9 = 3.2/8 , prop theorem as TS is parallel to MP

y = 3.6

4. MR/TS = 10/4 = 2.5

RT/SN = 9/3.6 = 2.5

MT/TN = 8/3.2 = 2.5

Therefore as the ratio is same, MRT is similar to TSN
by Diamond (43,720 points)

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