Question

Students in Mrs. Marquez's class are watching a film on the uses of geometry

Answer 1

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 $\overline {AD}$ on ΔABD are congruent to ∠CBD, ∠BDC, and

segment $\overline {CD}$ on ΔCBD, therefore, ΔABD ≅ ΔCBD, by AAS Theorem

Reasons:

The figure of the projector that casts an image on the screen is attached.

The bisector of the line $\overline {AC}$ = $\overline {BD}$

From the drawing, we have;

∠ABD ≅ ∠CBD by equal number arc mark.

The two column proof is therefore, presented as follows;

Statement ${}$                                            Reason

$\overline {BD}$ is perpendicular bisector of   ${}$$\overline {AC}$   Given

$\overline {AD}$ = $\overline {CD}$   ${}$                                             Definition of bisected line $\overline {AC}$  

∠BDC = 90°       ${}$                                      $\overline {BD}$ is perpendicular $\overline {AC}$  

∠BDA = 90°                         ${}$                    $\overline {BD}$ is perpendicular $\overline {AC}$  

∠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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