Prove the following # Prove the Following:## Given:- \( \overline{AC} \perp \overline{BD} \), D is the midpoint of \( \overline{AC} \)## Prove:- \( \triangle ABD \cong \triangle CBD \)### Diagram Explanation:The diagram shows a rectangle with points A, B, C, D. Lines AD and DC are diagonals intersecting at point D, creating right angles with line BD.### Proof Steps:| Statement | Reason ||------------------------------------------------|----------------------------------------------|| 1. \( \overline{AC} \perp \overline{BD} \), D is the midpoint of \( \overline{AC} \) | 1. Given || 2. \( \angle ADB \) & \( \angle CDB \) are right angles | 2. Definition of Perpendicular Lines || 3. All right angles are congruent | 3. || 4. \( \overline{AD} \cong \overline{DC} \) | 4. Definition of Midpoint || 5. DB \( \cong \) DB | 5. Reflexive Property || 6. \( \triangle ABD \cong \triangle CBD \) | 6. SAS (Side-Angle-Side) |### Key:- **Given**: Information that is provided as part of the problem.- **Definition of Midpoint**: The midpoint divides a line into two equal segments.- **Definition of Perpendicular Lines**: Perpendicular lines intersect to form right angles.- **Reflexive Property**: Any geometric quantity is equal to itself.- **SAS (Side-Angle-Side)**: A rule stating if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Name: Prove the following # Prove the Following:## Given:- \( \overline{AC}
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Prove the following # Prove the Following:## Given:- \( \overline{AC} \perp \overline{BD} \), D is the midpoint of \( \overline{AC} \)## Prove:- \( \triangle ABD \cong \triangle CBD \)### Diagram Explanation:The diagram shows a rectangle with points