Question

drag each statement to the correct location on the flowchart. not all statements will be used. given: $overline{ab} parallel overline{cd}$ and $overline{ad} parallel overline{bc}$ prove: $angle a cong angle c$ complete the flowchart proof. $mangle abc = mangle abd + mangle cbd$ $mangle dab = mangle bcd$ $mangle adc = mangle adb + mangle cdb$ $mangle dab = mangle dac + mangle acd$ $mangle bcd = mangle dac + mangle acd$

Explanation:

Step1: Identify top substitution step

We use the angle addition for $\angle DAB$ and the congruent angle measure equality $\text{m}\angle BAC = \text{m}\angle ACD$ to substitute.
$\text{m}\angle DAB = \text{m}\angle DAC + \text{m}\angle ACD$

Step2: Identify bottom substitution step

We use the angle addition for $\angle BCD$ and the congruent angle measure equality $\text{m}\angle DAC = \text{m}\angle BCA$ to substitute.
$\text{m}\angle BCD = \text{m}\angle DAC + \text{m}\angle ACD$

Step3: Final substitution step

Set the two expressions for $\text{m}\angle DAC + \text{m}\angle ACD$ equal to each other.
$\text{m}\angle DAB = \text{m}\angle BCD$

Answer:

Top dashed box: $\boldsymbol{\text{m}\angle DAB = \text{m}\angle DAC + \text{m}\angle ACD}$
Bottom dashed box: $\boldsymbol{\text{m}\angle BCD = \text{m}\angle DAC + \text{m}\angle ACD}$
Connecting dashed box (final substitution): $\boldsymbol{\text{m}\angle DAB = \text{m}\angle BCD}$