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AC is perpendicular to BD.
<h3>Further explanation</h3>- We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that
is reflexive.
- The length of the base of the triangle is the same, i.e.,
.
- In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely
. Thus we get ∠ACB = ∠ACD = 90°.
Conclusions for the SAS Congruent Postulate from this problem:
- ∠ACB = ∠ACD
- - - - - - - - - -
The following is not other or additional information along with the reasons.
- ∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and
- ∠BAC = ∠DAC no, because that is ASA with
- - - - - - - - - -
Notes
- The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
- The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.
- The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
- The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
- Which shows two triangles that are congruent by ASA? brainly.com/question/8876876
- Which shows two triangles that are congruent by AAS brainly.com/question/3767125
- About vertical and supplementary angles brainly.com/question/13096411