Question

Geometry help? I need step by step instructions on how to do each problem.

Answer 1

Answer:

See solution

Step-by-step explanation:

Similar triangles have proportional corresponding sides.

1.

$\dfrac{x}{5}=\dfrac{3}{3+3}\Rightarrow 6x=15,\ x=\dfrac{5}{2}=2.5.$

2.

$\dfrac{x}{18}=\dfrac{15}{15+7.5}\Rightarrow 22.5x=15\cdot 18,\ x=\dfrac{270}{22.5}=12.$

3.

$\dfrac{x}{5}=\dfrac{8+4}{4}\Rightarrow 4x=60,\ x=\dfrac{60}{4}=15.$

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.