Question

complete the proof by choosing the correct reason. given: m∠etg = m∠hk, m∠2 = m∠4. prove: m∠1 = m∠3. 1. m∠etg = m∠1 - m∠2 - some addition property. 2. m∠hk = m∠3 + m∠4 - angle addition property. 3. m∠etg = m∠hk - given. 4. m∠1 - m∠2 = m∠3 - m∠4 - subtraction property. 5. m∠2 = m∠4 - given. 6. m∠1 - m∠4 = m∠3 - m∠4 - angle addition property.

Explanation:

Step1: Express ∠ETG as sum of angles

$m\angle ETG=m\angle1 + m\angle2$ (Angle - Addition Property)

Step2: Express ∠ETH as sum of angles

$m\angle ETH=m\angle3 + m\angle4$ (Angle - Addition Property)

Step3: Use the given equality

Since $m\angle ETG = m\angle ETH$ (Given)
We have $m\angle1 + m\angle2=m\angle3 + m\angle4$ (Substitution Property)

Step4: Use the other given equality

Given $m\angle2 = m\angle4$
Substitute $m\angle2$ with $m\angle4$ in the equation $m\angle1 + m\angle2=m\angle3 + m\angle4$
We get $m\angle1 + m\angle4=m\angle3 + m\angle4$

Step5: Subtract $m\angle4$ from both sides

$m\angle1=m\angle3$ (Subtraction Property of Equality)

Answer:

$m\angle1=m\angle3$