Question

use the given information to prove that m∠aec = m∠bed. given: m∠1 = m∠3 prove: m∠aec = m∠bed

Explanation:

Step1: Analyze Angle Composition

$\angle AEC$ is composed of $\angle 1$ and $\angle 2$ (i.e., $m\angle AEC = m\angle 1 + m\angle 2$), and $\angle BED$ is composed of $\angle 2$ and $\angle 3$ (i.e., $m\angle BED = m\angle 2 + m\angle 3$).

Step2: Substitute Given Equality

We know from the given that $m\angle 1 = m\angle 3$. Substitute $m\angle 1$ with $m\angle 3$ in the expression for $m\angle AEC$: $m\angle AEC = m\angle 3 + m\angle 2$.

Step3: Compare Angles

Now, $m\angle AEC = m\angle 2 + m\angle 3$ and $m\angle BED = m\angle 2 + m\angle 3$. By the transitive property of equality, $m\angle AEC = m\angle BED$.

Answer:

By analyzing angle composition ($\angle AEC = \angle 1 + \angle 2$, $\angle BED = \angle 2 + \angle 3$) and substituting $m\angle 1 = m\angle 3$ (given), we conclude $m\angle AEC = m\angle BED$.