Given:
The circles passing through point
are centered at points
and
and have radii of length
.
The circle passing through points
and
is centered at point
.
Line A B. Two circle arcs with the same radius centered at point B intersect line A B to create points C and D. Point C is outside points A and B. Point D is between points A and B. Two circle arcs, one centered at point C and one centered at point D intersect through a point E, creating line B E. Angle D B E is labeled one. Angle C B E is labeled two.
Line A B. Two circle arcs with the same radius centered at point B intersect line A B to create points C and D. Point C is outside points A and B. Point D is between points A and B. Two circle arcs, one centered at point C and one centered at point D intersect through a point E, creating line B E. Angle D B E is labeled one. Angle C B E is labeled two.
Complete the proof that
.
Step Statement Reason
1


All radii of the same circle have the same length.
2
Both circles have radii of the same length.
3
They're lengths of the same segment.
4
Side-side-side congruence (1, 2, 3)
5
Corresponding parts of congruent triangles are congruent (4).
6
Angles are congruent if and only if they have the same measure (5).
7
The measures of


angles sum to
.
8


Substitution (6, 7)
9
Collect like terms (8).
10
Divide b