Math Problem Statement

Given: The circle centered at point [A] has a radius of length [AB]. The circles centered at points [B] and [D] have radii of length [DE]. Ray A B and ray A C intersect at point A. A circle arc centered at point A interesects point B on ray A B and point D on ray A C. One circle arc centered at point B and one circle arc centered at point D intersect at point A and point E. A ray connects points A and E so that rays A B, A D, and A E all start at point A. [A] [B] [C] [D] [E] Complete the proof that [\angle DAE \cong \angle BAE]. Step Statement Reason 1 [AB=AD] All radii of the same circle have the same length. 2

Both circles have radii of the same length. 3 [AE=AE] They're lengths of the same segment. 4

Side-side-side congruence (1, 2, 3) 5 [\angle DAE \cong \angle BAE] Corresponding parts of congruent triangles are congruent (4).

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Congruence
Triangles
Circle Properties

Formulas

Reflexive property (AE = AE)
SSS (Side-Side-Side) Triangle Congruence
CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Theorems

SSS Triangle Congruence
CPCTC (Corresponding Parts of Congruent Triangles)

Suitable Grade Level

Grades 9-12