Answer:
See solution
Step-by-step explanation:
Similar triangles have proportional corresponding sides.
1.
[tex]\dfrac{x}{5}=\dfrac{3}{3+3}\Rightarrow 6x=15,\ x=\dfrac{5}{2}=2.5.[/tex]
2.
[tex]\dfrac{x}{18}=\dfrac{15}{15+7.5}\Rightarrow 22.5x=15\cdot 18,\ x=\dfrac{270}{22.5}=12.[/tex]
3.
[tex]\dfrac{x}{5}=\dfrac{8+4}{4}\Rightarrow 4x=60,\ x=\dfrac{60}{4}=15.[/tex]
4. Angles ACB and ECD are congruent as vertical angles. Angles BAC and DEC are congruent (given), then ΔABC and ΔEDC are similar by AA theorem.
5. MN=NP=8 (given), NR=NQ=8+10=18 (given), angle N is common, then ΔNMP and ΔNQR are similar by SAS theorem.
