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Are the triangles shown in the Brazilian flag congruent by the ASA Congruence Theorer O no yes

Are the triangles shown in the Brazilian flag congruent by the ASA Congruence Theorer O no yes

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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**Understanding Congruence in Geometry: Brazilian Flag Example** In this lesson, we explore the concept of triangle congruence using the ASA (Angle-Side-Angle) Congruence Theorem. Let us examine an illustrative example involving the Brazilian flag. ### Question: Are the triangles shown in the Brazilian flag congruent by the ASA Congruence Theorem? ### Visual Representation: In the Brazilian flag image, triangles have been outlined in black. These triangles are created by drawing lines connecting specific points inside the diamond shape, intersecting at the circle's center. ### Options: - O no - O yes ### Explanation: The ASA (Angle-Side-Angle) Congruence Theorem states that if two triangles have two angles and the included side equal, then the triangles are congruent. To determine if the triangles within the Brazilian flag meet this criterion, one would need to verify: - The measure of two angles and the length of the included side in each triangle. - Compare these elements between the triangles. In your evaluation: 1. Identify the two pairs of angles that are equal. 2. Confirm that the side between these angles (the included side) is of equal length in both triangles. ### Conclusion: Based on the visual evidence provided by the image, you can derive whether the triangles are congruent via the ASA Congruence Theorem. When ready, select the appropriate answer. By engaging with real-world examples like national flags, learners gain a deeper understanding and appreciation of geometric principles in their everyday surroundings.
Transcribed Image Text:**Understanding Congruence in Geometry: Brazilian Flag Example** In this lesson, we explore the concept of triangle congruence using the ASA (Angle-Side-Angle) Congruence Theorem. Let us examine an illustrative example involving the Brazilian flag. ### Question: Are the triangles shown in the Brazilian flag congruent by the ASA Congruence Theorem? ### Visual Representation: In the Brazilian flag image, triangles have been outlined in black. These triangles are created by drawing lines connecting specific points inside the diamond shape, intersecting at the circle's center. ### Options: - O no - O yes ### Explanation: The ASA (Angle-Side-Angle) Congruence Theorem states that if two triangles have two angles and the included side equal, then the triangles are congruent. To determine if the triangles within the Brazilian flag meet this criterion, one would need to verify: - The measure of two angles and the length of the included side in each triangle. - Compare these elements between the triangles. In your evaluation: 1. Identify the two pairs of angles that are equal. 2. Confirm that the side between these angles (the included side) is of equal length in both triangles. ### Conclusion: Based on the visual evidence provided by the image, you can derive whether the triangles are congruent via the ASA Congruence Theorem. When ready, select the appropriate answer. By engaging with real-world examples like national flags, learners gain a deeper understanding and appreciation of geometric principles in their everyday surroundings.
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