Answer:
The 3 truth relationships are:
Line CD is the perpendicular bisector of AB ⇒ (1)
Line AB is perpendicular to the line CD ⇒ (3)
Line segment AE is congruent to line segment BE ⇒ (4)
Step-by-step explanation:
<em>When two circles </em><em>pass through the centers of each other</em><em>, then the line </em><em>joining their intersection points</em><em> is the </em><em>axis of symmetry (perpendicular bisector) </em><em>of the </em><em>segment joining their centers</em>
In the given figure
∵ Circle A passes through the center of circle B
∵ Circle B passes through the center of circle A
∴ AB is the line center
∵ Circles A and B intersected at points C and D
∴ CD is the line joining their intersection points
→ By using the rule above
∴ CD is the perpendicular bisector of AB
∴ Line CD is the perpendicular bisector of AB ⇒ (1)
∵ CD ⊥ AB
→ That means AB is perpendicular to CD
∴ Line segment AB is perpendicular to line CD ⇒ (3)
∵ CD is the perpendicular bisector of AB
∴ E is the mid-point of AB
→ That means E divides AB into two equal parts AE and BE
∴ AE = BE
∴ Line segment AE is congruent to line segment BE ⇒ (4)
