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What 3 relationships are truth in the construction below?? (Only if you know please though! I numbered them for you as well!)

What 3 relationships are truth in the construction below?? (Only if you know please-example-1

1 Answer

4 votes

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)

Explanation:

When two circles pass through the centers of each other, then the line joining their intersection points is the axis of symmetry (perpendicular bisector) of the segment joining their centers

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)

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