Question

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

Answer 1

See solution

Explanation:

Similar triangles have proportional corresponding sides.

1.

`(x)/(5)=(3)/(3+3)\Rightarrow 6x=15,\ x=(5)/(2)=2.5.`

2.

`(x)/(18)=(15)/(15+7.5)\Rightarrow 22.5x=15\cdot 18,\ x=(270)/(22.5)=12.`

3.

`(x)/(5)=(8+4)/(4)\Rightarrow 4x=60,\ x=(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.