The completed statement is presented as follows;
The figure has rotational symmetry about point B because rotating it 180° about point B maps ∆AEB unto ∆DCB. The figure has two lines of symmetry, because point E is the same distance but in opposite direction from point B as point C. and point E is the same distance but in opposite direction from point B as point A
What type of symmetry are in the figure?
The properties of the figure are:
Side AB and BE in ∆AEB are congruent to sides BD and BC in ∆DCB
Angle ⟨ABE and ⟨CBD are congruent according to vertical angle postulate
Therefore;
∆AEB is congruent to ∆DCB. by Side–Angle–Side, SAS, congruency postulate
Rotation of the figure 180° about B maps ∆AEB to ∆DCB.
Therefore;
The figure comprises of two congruent triangles, because rotating ∆AEB gives
∆DCB
Therefore;
The figure has rotational symmetry about point B because rotating it 180° about point B maps ∆AEB unto ∆DCB
Similarly, the figure has two lines of symmetry, because point E is the same distance but in opposite direction from point B as point C. and point E is the same distance but in opposite direction from point B as point A.
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