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}
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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

Provides figure is AC¯ ⊥ BD¯ D is the midpoint of AC¯. To prove: ∆ABD≅∆CBD

Answered: Prove the following: Given: AC1 BD,D is…

Math

Geometry

Prove the following: Given: AC1 BD,D is the midpoint of AC Prove: AABD = ACBD A

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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