Answer:
[tex]\begin{gathered} d)\text{The angles in ABC have the same measures as the angles in DEF} \\ \text{The radio of corresponding sides lengths are equal }to\text{ each other} \\ \text{The triangles are similar} \\ c)\text{ }\frac{AB}{DE}=\frac{12}{6}=2 \\ \frac{BC}{EF}=\frac{6}{3}=2 \\ \frac{CA}{FD}=\frac{10}{5}=2 \end{gathered}[/tex]
Step-by-step explanation:
Make a diagram with the given information:
Since the sum of all intern angles of a triangle must add up to 180°, and you have two angles of each one:
[tex]\begin{gathered} Assuming you did the measure of the lengths correctly with the rule:[tex]\begin{gathered} AB=12,\text{ B}C=6,\text{ }CA=10 \\ DE=6,\text{ }EF=3,\text{ FD=}5 \\ \end{gathered}[/tex]
c) The ratio for the sides is the relation between the sides:
[tex]\begin{gathered} \frac{AB}{DE}=\frac{12}{6}=2 \\ \frac{BC}{EF}=\frac{6}{3}=2 \\ \frac{CA}{FD}=\frac{10}{5}=2 \end{gathered}[/tex]
d) For the given statements:
[tex]\begin{gathered} \text{The angles in ABC have the same measures as the angles in DEF} \\ \text{The radio of corresponding sides lengths are equal }to\text{ each other} \\ \text{The triangles are similar} \end{gathered}[/tex]
