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The given information on the diagram of the projector and the image can
be used to prove the congruency of the triangles.
∠ABD, ∠BDA, and side on ΔABD are congruent to ∠CBD, ∠BDC, and
segment on ΔCBD, therefore, ΔABD ≅ ΔCBD, by <u>AAS Theorem</u>
Reasons:
The figure of the projector that casts an image on the screen is attached.
The bisector of the line =
From the drawing, we have;
∠ABD ≅ ∠CBD by equal number arc mark.
The two column proof is therefore, presented as follows;
Statement Reason
is perpendicular bisector of
Given
=
Definition of bisected line
∠BDC = 90°
is perpendicular
∠BDA = 90°
is perpendicular
∠ABD ≅ ∠CBD Given on the diagram
ΔABD ≅ ΔCBD by Angle-Angle-Side AAS Congruency rule
The Angle-Angle-Side, AAS, Congruency postulate states that two
triangles are congruent where two adjacent angles and a non included side
on one triangle are congruent to the corresponding two adjacent angles
and a non included side on the other triangle.
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