This is a geometry question. **Given:**- $ABCD$ is a parallelogram.- $\overline{DE} \perp \overline{AC}$- $\overline{BF} \perp \overline{AC}$**Prove:**- $DEBF$ is a rectangle.**Diagram Explanation:**The provided diagram depicts parallelogram $ABCD$. In this parallelogram:- Point $E$ and point $F$ are marked such that $\overline{DE}$ and $\overline{BF}$ are both perpendicular to the diagonal $\overline{AC}$, forming right angles $\angle DEC$ and $\angle BFA$ respectively.The objective is to prove that quadrilateral $DEBF$ forms a rectangle. In order to establish this, it is critical to show that:1. Opposite sides of $DEBF$ are parallel and equal.2. Each of the angles in $DEBF$ is a right angle. Given the information, the perpendicular lines to the diagonal and the parallelogram properties should be employed in proving this assertion.

Answered: Given: ABCD3; D. DE I AC: BF I AC…

Math

Geometry

Given: ABCD3; D. DE I AC: BF I AC Prove: DEBF is 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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This is a geometry question.

**Given:**
- $ABCD$ is a parallelogram.
- $\overline{DE} \perp \overline{AC}$
- $\overline{BF} \perp \overline{AC}$

**Prove:**
- $DEBF$ is a rectangle.

**Diagram Explanation:**
The provided diagram depicts parallelogram $ABCD$. In this parallelogram:
- Point $E$ and point $F$ are marked such that $\overline{DE}$ and $\overline{BF}$ are both perpendicular to the diagonal $\overline{AC}$, forming right angles $\angle DEC$ and $\angle BFA$ respectively.

The objective is to prove that quadrilateral $DEBF$ forms a rectangle. In order to establish this, it is critical to show that:
1. Opposite sides of $DEBF$ are parallel and equal.
2. Each of the angles in $DEBF$ is a right angle.

Given the information, the perpendicular lines to the diagonal and the parallelogram properties should be employed in proving this assertion.

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