Question

given: line $overleftrightarrow{ab}$ intersects line $overleftrightarrow{dc}$ at point $e$; $angle aeb$ and $angle dec$ are straight angles. prove: $angle aeccongangle deb$. statements 1. 2. $angle aec$ is supplementary to $angle ceb$. 3. $angle deb$ is supplementary to $angle ceb$. 3. def. of supplementary $angle s$ 4. reasons 1. 2. 4. $cong$ supplements theorem a. $angle aeb$ and $angle dec$ are straight angles. b. substitution c. angle addition postulate d. given e. addition property of equality f. linear pair theorem g $angle aec$ is congruent to $angle deb$ h. def. supplementary angles

Explanation:

Step1: State given information

1. Statements: $\angle AEB$ and $\angle DEC$ are straight angles. Reasons: Given

Step2: Identify supplementary - angle relationships

1. Statements: $\angle AEC$ is supplementary to $\angle CEB$. Reasons: Linear Pair Theorem
2. Statements: $\angle DEB$ is supplementary to $\angle CEB$. Reasons: Def. of Supplementary $\angle s$

Step3: Apply congruent - supplements theorem

1. Statements: $\angle AEC\cong\angle DEB$. Reasons: $\cong$ Supplements Theorem

Answer:

1. Statements: $\angle AEB$ and $\angle DEC$ are straight angles. Reasons: d. Given
2. Reasons: f. Linear Pair Theorem
3. Statements: $\angle AEC\cong\angle DEB$. Reasons: $\cong$ Supplements Theorem