Answer:
Part A. Option 4
Part B. Option 3
Step-by-step explanation:
A. To solve this question we will find all sides of rectangles PQRS and JKLM
m PQ = m RS = 9 -5 = 4
m QR = m SP = 12 - 7 = 5
m JK = m LM = 6 - 4 = 2
m MJ = m KL = 10 - 5 = 5
Now for option 1).
[tex]\frac{PQ}{QR}=\frac{4}{5}[/tex]
[tex]\frac{JK}{LM}=\frac{2}{2}[/tex]
So incorrect.
Option 2).
[tex]\frac{SP}{SR}=\frac{5}{4}[/tex]
[tex]\frac{MJ}{ML}=\frac{5}{2}[/tex]
So incorrect option.
Option 3).
[tex]\frac{PQ}{QR}=\frac{4}{5}[/tex]
[tex]\frac{JK}{KL}=\frac{2}{5}[/tex]
Option 4).
[tex]\frac{SR}{ML}=\frac{4}{2}[/tex]
[tex]\frac{PQ}{JK}=\frac{4}{2}[/tex]
So both the ratios are same.
Option 4 shows the same ratio of corresponding sides therefore, both the rectangular tiles are similar.
Part B.
In this part of the question we have to find the inequality which will contradict the assumption.
If DE is parallel to BC, then ΔADE and ΔABC will be similar and by the law of similarity
[tex]\frac{AB}{DE}=\frac{AC}{AE}[/tex]
[tex]\frac{8}{5}=\frac{10}{6}[/tex]
[tex]\frac{5}{8}=\frac{6}{10}[/tex]
Therefore, the inequality which contradict the assumption is Option 3.
