Math  /  Geometry

QuestionGiven: ADDC\overline{A D} \cong \overline{D C} and ABBC\overline{A B} \cong \overline{B C}. Prove: ACBD\overline{A C} \perp \overline{B D}.
Step
1 Statement ADDC\overline{A D} \cong \overline{D C} ABBC\overline{A B} \cong \overline{B C}
Reason
Given try Type of Statement
Note: AC\overline{A C} and BD\overline{B D} are segments.

Studdy Solution
Since ABDCBD \triangle ABD \cong \triangle CBD , the angles ADB \angle ADB and CDB \angle CDB are congruent. This implies that the diagonals AC AC and BD BD bisect each other at right angles.
The diagonals AC AC and BD BD are perpendicular, thus:
ACBD \overline{AC} \perp \overline{BD}

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