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D. 2) Given: LA LB Supplamentans SA; LD a paratletogram B. prove: ABCDIS parallelogram ABICD Statement Reason ) given. CA TWAI SI

D. 2) Given: LA LB Supplamentans SA; LD a paratletogram B. prove: ABCDIS parallelogram ABICD Statement Reason ) given. CA TWAI SI

Elementary Geometry For College Students, 7e
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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I have to prove it by doing a statement and reason chart, as seen below. 

**Proving Parallelograms: Example Problem** In this example, we are given certain angle relationships and are asked to prove that a quadrilateral is a parallelogram based on these relationships. **Problem Statement:** Given: 1. \( \angle A \) and \( \angle B \) are supplementary. 2. \( \angle A \) is adjacent to \( \angle D \). To Prove: \( ABCD \) is a parallelogram, given that \( AB \cong CD \) (AB is congruent to CD). **Diagram Explanation:** On the right side of the notebook sheet, there is a diagram of the quadrilateral ABCD. Here is a breakdown of the diagram: - Quadrilateral \(ABCD\) is drawn, indicating points \(A\), \(B\), \(C\), and \(D\). - Sides \(AB\) and \(CD\) are marked to indicate that they are equal in length (denoted by the congruency symbol \( \cong \)). **Proof Structure:** A two-column proof structure will be used to demonstrate this mathematical proof. The two columns will be labeled "Statement" and "Reason" respectively. ``` | Statement | Reason | |-----------|--------| | 1) | 1) given | ``` **Explanation:** 1. The given information forms the basis of the proof. 2. \( \angle A \) and \( \angle B \) are supplementary, meaning their sum is 180 degrees. 3. \( \angle A \) is adjacent to \( \angle D \). Using these angle relationships and the property that opposite sides of a parallelogram are equal in length, we will show that \( ABCD \) must be a parallelogram. **Note:** This problem and proof are intended for educational purposes to illustrate how angle and side relationships can be used to determine that a quadrilateral is a parallelogram. Further steps and justifications (not shown here) would complete the proof in a typical classroom setting.
Transcribed Image Text:**Proving Parallelograms: Example Problem** In this example, we are given certain angle relationships and are asked to prove that a quadrilateral is a parallelogram based on these relationships. **Problem Statement:** Given: 1. \( \angle A \) and \( \angle B \) are supplementary. 2. \( \angle A \) is adjacent to \( \angle D \). To Prove: \( ABCD \) is a parallelogram, given that \( AB \cong CD \) (AB is congruent to CD). **Diagram Explanation:** On the right side of the notebook sheet, there is a diagram of the quadrilateral ABCD. Here is a breakdown of the diagram: - Quadrilateral \(ABCD\) is drawn, indicating points \(A\), \(B\), \(C\), and \(D\). - Sides \(AB\) and \(CD\) are marked to indicate that they are equal in length (denoted by the congruency symbol \( \cong \)). **Proof Structure:** A two-column proof structure will be used to demonstrate this mathematical proof. The two columns will be labeled "Statement" and "Reason" respectively. ``` | Statement | Reason | |-----------|--------| | 1) | 1) given | ``` **Explanation:** 1. The given information forms the basis of the proof. 2. \( \angle A \) and \( \angle B \) are supplementary, meaning their sum is 180 degrees. 3. \( \angle A \) is adjacent to \( \angle D \). Using these angle relationships and the property that opposite sides of a parallelogram are equal in length, we will show that \( ABCD \) must be a parallelogram. **Note:** This problem and proof are intended for educational purposes to illustrate how angle and side relationships can be used to determine that a quadrilateral is a parallelogram. Further steps and justifications (not shown here) would complete the proof in a typical classroom setting.
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