Chapter 2.5, Problem 1PSA

a)

To determine

To calculate: To identify congruent angle or segments

Answer to Problem 1PSA

  $\angle AEB=\angle ABE$ And $\angle ADC=\angle ACD\&\angle DEB=\angle CBE$

Explanation of Solution

Given information: $AE=AB\text{}$ And $ED=BC\text{}$ .

using properties of parallel lines and properties of triangles,

  $AE=AB\Rightarrow \angle AEB=\angle ABE.$

Also,

  $\begin{array}{l}AE+ED=AB+BC\\ \therefore AD=AC.\Rightarrow \angle ADC=\angle ACD.\end{array}$

By linear pair axiom, $\angle DEB=\angle CBE.$

b)

To determine

To calculate: To identify congruent angle or segments

Answer to Problem 1PSA

  $FG=JH\text{}$ And $IF=GH\text{}$

Explanation of Solution

Given information: $\angle JHF=\angle GFH\&\angle JFH=\angle GHF.$

using properties of parallel lines and properties of triangles,

b) $\angle JHF=\angle GFH.$ And $\angle JFH=\angle GHF.$

  $\Rightarrow JH\parallel FG$ And $FJ\parallel FH.$

Hence FGHJ is a parallelogram, therefore opposite sides are equal.