Answer:
Part 1) Triangle GHI, JKL
Part 2) [tex](40*15)and(8*3)[/tex], [tex](18*6)and(4.5*1.5)[/tex]
Step-by-step explanation:
we know that
If two figures are similar
then
the ratio of their corresponding sides are equal and is called the scale factor
Part 1)
case a) triangle GHI
If ABC and GHI are similar
then
[tex]\frac{4}{24}=\frac{3}{7}=\frac{5}{25}[/tex]
but
[tex]0.17 \neq 0.43 \neq \ 0.20[/tex]
therefore
Triangle GHI is not similar to triangle ABC
case b) triangle DEF
If ABC and DEF are similar
then
[tex]\frac{4}{44}=\frac{3}{33}=\frac{5}{55}[/tex]
[tex]0.09=0.09=0.09[/tex]
therefore
Triangle DEF is similar to triangle ABC
case c) triangle MNO
If ABC and MNO are similar
then
[tex]\frac{4}{10}=\frac{3}{7.5}=\frac{5}{12.5}[/tex]
[tex]0.4=0.4=0.4[/tex]
therefore
Triangle MNO is similar to triangle ABC
case d) triangle JKL
If ABC and JKL are similar
then
[tex]\frac{4}{21}=\frac{3}{20}=\frac{5}{29}[/tex]
[tex]0.19 \neq 0.15 \neq 0.17[/tex]
therefore
Triangle JKL is not similar to triangle ABC
Part 2)
case a) If the rectangles are similar, then
[tex]\frac{40}{8}=\frac{15}{3}[/tex]
[tex]5=5[/tex]
therefore
the rectangles are similar
case b) If the rectangles are similar, then
[tex]\frac{18}{4.5}=\frac{6}{1.5}[/tex]
[tex]4=4[/tex]
therefore
the rectangles are similar
case c) If the rectangles are similar, then
[tex]\frac{1,225}{3.5}=\frac{144}{1.2}[/tex]
[tex]350\neq120[/tex]
therefore
the rectangles are not similar
case d) If the rectangles are similar, then
[tex]\frac{13}{5.2}=\frac{5}{2.5}[/tex]
[tex]2.5\neq 2[/tex]
therefore
the rectangles are not similar