Question

Please help!! Need to get this done

Answer 1

Given:

Segment AD is perpendicular to segment BC.

D is the midpoint of segment BC.

To prove:

$\Delta BDA\cong \Delta CDA$

Solution:

The two column proof is shown below:

Statements                                                      Reasons

1. $\overline{AD}\perp \overline{BC}$, D is the midpoint of $\overline{BC}$         1. Given

2. $\overline{BD}\cong \overline{CD}$                                                 2. Definition of midpoint

3. $m\angle ADB=90^\circ \text{ and }m\angle ADC=90^\circ$         3. Definition of perpendicular lines

4. $m\angle ADB=m\angle ADC$                                4. Substitution

5. $m\angle ADB\cong m\angle ADC$                                5. Definition of congruence

6. $\overline{AD}\cong \overline{AD}$                                                 6. Reflexive property

7. $\Delta BDA\cong \Delta CDA$                                      7. SAS congruence postulate

Hence proved.