|
|
1. A perpendicular bisector of a segment (by definition) is a line that is perpendicular to the segment and intersects the segment at its midpoint.
|
2.  because a midpoint of a segment divides the segment into two congruent segments.
|
3. AD = DB because congruent segments are segments of equal measure.
|
4. The line of reflection for a segment is the perpendicular bisector of the segment.
|
5. Under a reflection in  , A is mapped onto B, C is mapped onto C, and D is mapped onto D.
|
6. Under a reflection in  ,  is mapped onto  .
|
7. CA = CB since a reflection is a rigid transformation which preserves length. |
Statements |
Reasons |
1.  |
1. Given |
2.  |
2. Segment bisector forms 2 congruent segments. |
3. ∠ADC, ∠BDC are right angles |
3. Perpendiculars form right angles. |
4. ∠ADC ∠BDC |
4. All right angles are congruent. |
5.  |
5. Reflexive property |
6.  |
6. SAS: If 2 sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
7.  |
7. CPCTC: Corresponding parts of congruent triangles are congruent. |
8. CA = CB |
8. Congruent segments have equal measure. |