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Here are two triangles E А В Aro thoco triangloc cimilar? Oce tri. conar +2Explain bow woI

Here are two triangles E А В Aro thoco triangloc cimilar? Oce tri. conar +2Explain bow woI

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Here are two triangles** The diagram displays two triangles, △ABC and △DBE, arranged with a shared vertex B. Triangle △ABC has right angle ∠CAB, and triangle △DBE has right angle ∠BDE. Both triangles share angle ∠CBE. **Question:** Are these triangles similar? Are these triangles congruent? Explain how you know for each. **Explanation:** Triangles are similar if they have the same shape, which means they have proportional sides and equal angles. Triangles are congruent if they are identical in shape and size, meaning all corresponding sides and angles are equal. To determine similarity and congruence, we can explore the following: 1. **Angle-Angle (AA) Similarity:** - Both triangles have a right angle (∠CAB and ∠BDE). - They share angle ∠CBE. - Since two angles are equal, the triangles are similar by AA similarity. 2. **Side lengths and angles for Congruence:** - For the triangles to be congruent, all corresponding sides and angles must be equal. - Without specific side measurements, we cannot use criteria like Side-Angle-Side (SAS) or Side-Side-Side (SSS) to prove congruence just based on the given diagram. Therefore, based on the information provided, the triangles are similar but not necessarily congruent without more information on side lengths.
Transcribed Image Text:**Here are two triangles** The diagram displays two triangles, △ABC and △DBE, arranged with a shared vertex B. Triangle △ABC has right angle ∠CAB, and triangle △DBE has right angle ∠BDE. Both triangles share angle ∠CBE. **Question:** Are these triangles similar? Are these triangles congruent? Explain how you know for each. **Explanation:** Triangles are similar if they have the same shape, which means they have proportional sides and equal angles. Triangles are congruent if they are identical in shape and size, meaning all corresponding sides and angles are equal. To determine similarity and congruence, we can explore the following: 1. **Angle-Angle (AA) Similarity:** - Both triangles have a right angle (∠CAB and ∠BDE). - They share angle ∠CBE. - Since two angles are equal, the triangles are similar by AA similarity. 2. **Side lengths and angles for Congruence:** - For the triangles to be congruent, all corresponding sides and angles must be equal. - Without specific side measurements, we cannot use criteria like Side-Angle-Side (SAS) or Side-Side-Side (SSS) to prove congruence just based on the given diagram. Therefore, based on the information provided, the triangles are similar but not necessarily congruent without more information on side lengths.
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