A: linear pair postulateB: angle addition postulate with angles forming a straight angleC: definition of supplementaryD: triangle sum theorem ## Question 6### What is the reason for the statement in step 3?**Given:** \( B \) is a point on \( \overline{AC} \) and \( \angle D\), \( \angle E\), and \( \angle DBE \) are right angles.**Prove:** \( \triangle ADB \sim \triangle BEC \)### Diagram Explanation:The diagram shows two right triangles and a point \( B \) on line \( \overline{AC} \):- **Triangle \( ADB \):** - \( \angle D \) is a right angle (90°). - \( ADB \) is positioned on the left side of \( \overline{AC} \) with the right angle at \( D \).- **Triangle \( BEC \):** - \( \angle E \) is a right angle (90°). - \( BEC \) is on the right side of \( \overline{AC} \) with the right angle at \( E \).Both triangles share the same line \( \overline{AC} \), extending in different directions through point \( B \). ### Statements and Reasons Table:| Statements | Reasons ||----------------------------------------------------|--------------------------------|| 1. Point \( B \) is on \( \overline{AC} \). | Given || \( \quad \angle D\), \( \angle E\), and \( \angle DBE \) are right angles. | Given || 2. \( m \angle D = m \angle E = m \angle DBE = 90^\circ \) | Definition of right angle || 3. | |**Explanation of Step 3 Needed Here:**To complete step 3 in proving the similarity of triangles \( \triangle ADB \sim \triangle BEC \), we need to use criteria for triangle similarity, which could involve Angle-Angle (AA) criterion, Side-Angle-Side (SAS) criterion, or Side-Side-Side (SSS) criterion.### Conclusion:The similarity proof for \( \triangle ADB \sim \triangle BEC \) will require a specific reason for the third step, which generally might involve demonstrating the proportionality of sides or congruence of angles based on the given conditions and right angles throughout the ### Proof Table| Statements | Reasons ||----------------------------------------------------------------------------|------------------------------------------|| 1. Point B is on line AC | Given || 2. ∠D, ∠E, and ∠DBE are right angles | Given || 3. m∠D = m∠E = m∠DBE = 90° | Definition of right angle || 4. m∠A + m∠D + m∠ABD = 180° | || 5. m∠C + m∠E + m∠CBE = 180° | || 6. m∠ABD + m∠DBE + m∠CBE = 180° | Substitution || 7. m∠A + 90° + m∠ABD = 180° | || 8. m∠C + 90° + m∠CBE = 180° | Substitution Property of Equality || 9. m∠ABD + 90° = m∠CBE = 180° | || 10. m∠A + m∠ABD = 90° | Subtraction Property of Equality || 11. m∠C + m∠CBE = 90° | || 12. m∠ABD + m∠CBE = 90° | || 13. m∠ABD and m∠CBE are complementary | Definition of Complementary || 14. ∠C and ∠CBE are complementary | || 15. ∠C ≈ ∠CBE | || 16. ∠C ≈ ∠ABD | || 17. ∠ABD ≈ ∠BEC | |### Theory and PostulatesThe checkboxes at the bottom of the image refer to the following geometry concepts:- **A. Linear Pair Postulate**- **B. Angle Addition Postulate with Angles Forming a Straight Angle**- **C. Definition of Supplementary**

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Question 6 What is the reason for the statement in step 3? Given: B is a point on AC and ZD, ZE, and ZDBE are right angles. Prove: Δ ADB ~ Δ BEC E D 1. 2. Statements B Point is on AC ZD, ZE, and ZDRE are right angles m/D-m/E-m/DBE-90° Reasons Given Definition of right angle C

Question 6 What is the reason for the statement in step 3? Given: B is a point on AC and ZD, ZE, and ZDBE are right angles. Prove: Δ ADB ~ Δ BEC E D 1. 2. Statements B Point is on AC ZD, ZE, and ZDRE are right angles m/D-m/E-m/DBE-90° Reasons Given Definition of right angle C

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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