Question

match each sentence with the correct set-up. not all set-ups will be used. if ∠a and ∠b are vertical angles, then ____. if d is in the interior of ∠abc, then __. if m is the midpoint of $overline{ab}$, then __. if ∠a and ∠b form a linear pair, then __. if $overrightarrow{ad}$ bisects ∠bac, then ____. drag & drop the answer options: $mangle a + mangle b = 180^circ$, $mangle a + mangle b = 90^circ$, $angle a cong angle b$, $mangle a = mangle b$, $angle bad cong angle dac$, $mangle bad = mangle dac$, $mangle abd + mangle dbc = mangle abc$, $overline{am} cong overline{mb}$, $am = mb$, $mangle abc + mangle bcd = mangle abd$, $overline{ab} cong overline{bc}$, $ab = bc$

Explanation:

1. "If ∠A and ∠B are vertical angles, then ______"

• Vertical angles are equal in measure. So the correct match is "$\angle A \cong \angle B$, $m\angle A = m\angle B$".

2. "If D is in the interior of $\angle ABC$, then ______"

• By the Angle - Addition Postulate, if a point is in the interior of an angle, the sum of the measures of the two smaller angles formed is equal to the measure of the larger angle. So $m\angle ABD + m\angle DBC=m\angle ABC$.

3. "If M is the midpoint of $\overline{AB}$, then ______"

• The midpoint of a segment divides the segment into two congruent and equal - length segments. So $\overline{AM}\cong\overline{MB}$, $AM = MB$.

4. "If $\angle A$ and $\angle B$ form a linear pair, then ______"

• A linear pair of angles is supplementary, meaning their measures add up to $180^{\circ}$. So $m\angle A + m\angle B=180^{\circ}$.

5. "If $\overrightarrow{AD}$ bisects $\angle BAC$, then ______"

• An angle bisector divides an angle into two congruent angles with equal measures. So $\angle BAD\cong\angle DAC$, $m\angle BAD = m\angle DAC$.

Final Matches:

• "If ∠A and ∠B are vertical angles, then": $\boldsymbol{\angle A \cong \angle B}$, $\boldsymbol{m\angle A = m\angle B}$
• "If D is in the interior of $\angle ABC$, then": $\boldsymbol{m\angle ABD + m\angle DBC = m\angle ABC}$
• "If M is the midpoint of $\overline{AB}$, then": $\boldsymbol{\overline{AM}\cong\overline{MB}}$, $\boldsymbol{AM = MB}$
• "If ∠A and ∠B form a linear pair, then": $\boldsymbol{m\angle A + m\angle B = 180^{\circ}}$
• "If $\overrightarrow{AD}$ bisects $\angle BAC$, then": $\boldsymbol{\angle BAD\cong\angle DAC}$, $\boldsymbol{m\angle BAD = m\angle DAC}$

Answer:

1. "If ∠A and ∠B are vertical angles, then ______"

• Vertical angles are equal in measure. So the correct match is "$\angle A \cong \angle B$, $m\angle A = m\angle B$".

2. "If D is in the interior of $\angle ABC$, then ______"

• By the Angle - Addition Postulate, if a point is in the interior of an angle, the sum of the measures of the two smaller angles formed is equal to the measure of the larger angle. So $m\angle ABD + m\angle DBC=m\angle ABC$.

3. "If M is the midpoint of $\overline{AB}$, then ______"

• The midpoint of a segment divides the segment into two congruent and equal - length segments. So $\overline{AM}\cong\overline{MB}$, $AM = MB$.

4. "If $\angle A$ and $\angle B$ form a linear pair, then ______"

• A linear pair of angles is supplementary, meaning their measures add up to $180^{\circ}$. So $m\angle A + m\angle B=180^{\circ}$.

5. "If $\overrightarrow{AD}$ bisects $\angle BAC$, then ______"

• An angle bisector divides an angle into two congruent angles with equal measures. So $\angle BAD\cong\angle DAC$, $m\angle BAD = m\angle DAC$.

Final Matches:

• "If ∠A and ∠B are vertical angles, then": $\boldsymbol{\angle A \cong \angle B}$, $\boldsymbol{m\angle A = m\angle B}$
• "If D is in the interior of $\angle ABC$, then": $\boldsymbol{m\angle ABD + m\angle DBC = m\angle ABC}$
• "If M is the midpoint of $\overline{AB}$, then": $\boldsymbol{\overline{AM}\cong\overline{MB}}$, $\boldsymbol{AM = MB}$
• "If ∠A and ∠B form a linear pair, then": $\boldsymbol{m\angle A + m\angle B = 180^{\circ}}$
• "If $\overrightarrow{AD}$ bisects $\angle BAC$, then": $\boldsymbol{\angle BAD\cong\angle DAC}$, $\boldsymbol{m\angle BAD = m\angle DAC}$