Question

select the correct answer from each drop - down menu. in the figure, $overline{ab}paralleloverline{cd}$ and $angle eijcongangle gji$. complete the following statements to prove that $angle ikl$ and $angle jld$ are supplementary angles. it is given that $angle eijcongangle gji$. also, $angle eijcongangle ikl$ and $angle gjicongangle jlk$, as they are corresponding angles for parallel lines cut by a transversal. by the definition of congruent angles, $mangle eij = mangle gji$, $mangle eij = mangle ikl$, and $mangle gji = mangle jlk$. so, $mangle ikl = mangle jlk$ by the. angle $jlk$ and $angle jld$ are supplementary angles by the, so $mangle jlk + mangle jld = 180^{circ}$. by the, $mangle ikl + mangle jld = 180^{circ}$. therefore, $angle ikl$ and $angle jld$ are supplementary angles by definition.

Explanation:

Step1: Transitive property of equality

Since \(m\angle EIJ = m\angle GJI\), \(m\angle EIJ = m\angle IKL\), and \(m\angle GJI = m\angle JLK\), by the transitive - property of equality (if \(a = b\) and \(b = c\), then \(a = c\)), we have \(m\angle IKL=m\angle JLK\).

Step2: Definition of supplementary angles

\(\angle JLK\) and \(\angle JLD\) are supplementary angles because they are a linear - pair. By the definition of a linear pair of angles (two adjacent angles whose non - common sides are opposite rays), the sum of the measures of angles in a linear pair is \(180^{\circ}\), so \(m\angle JLK + m\angle JLD=180^{\circ}\).

Step3: Substitution property of equality

Since \(m\angle IKL = m\angle JLK\), we can substitute \(m\angle IKL\) for \(m\angle JLK\) in the equation \(m\angle JLK + m\angle JLD = 180^{\circ}\). By the substitution property of equality (if \(a = b\), then \(a\) can be substituted for \(b\) in any equation), we get \(m\angle IKL + m\angle JLD = 180^{\circ}\).

Answer:

First blank: Transitive property of equality
Second blank: Definition of a linear pair
Third blank: Substitution property of equality