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Geometry
C 3.

C 3.

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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**Goal: Prove the Triangle Sum Theorem** **Triangle Sum Theorem:** The three angle measures of a triangle add to 180°. **Goal:** To prove \( m1 + m2 + m3 = 180° \). ### Diagram Explanation The image shows a triangle, \( \triangle ABC \), with vertices labeled A, B, and C. There are three angles marked inside the triangle: - \( m1 \) at vertex A - \( m2 \) at vertex B - \( m3 \) at vertex C A line extends horizontally through point A and intersects lines AB and AC, creating two angles outside the triangle along this line, labeled as 4 and 5 at points X and Y. ### Proof Structure Below the diagram, there is a two-column table labeled "Statement" on the left and "Justification" on the right. The table is intended to be filled in to show a step-by-step proof of the Triangle Sum Theorem, using logical reasoning and geometric principles. The goal of this table is to guide students through constructing a formal proof that the sum of interior angles in triangle \( \triangle ABC \) equals 180°. ---
Transcribed Image Text:**Goal: Prove the Triangle Sum Theorem** **Triangle Sum Theorem:** The three angle measures of a triangle add to 180°. **Goal:** To prove \( m1 + m2 + m3 = 180° \). ### Diagram Explanation The image shows a triangle, \( \triangle ABC \), with vertices labeled A, B, and C. There are three angles marked inside the triangle: - \( m1 \) at vertex A - \( m2 \) at vertex B - \( m3 \) at vertex C A line extends horizontally through point A and intersects lines AB and AC, creating two angles outside the triangle along this line, labeled as 4 and 5 at points X and Y. ### Proof Structure Below the diagram, there is a two-column table labeled "Statement" on the left and "Justification" on the right. The table is intended to be filled in to show a step-by-step proof of the Triangle Sum Theorem, using logical reasoning and geometric principles. The goal of this table is to guide students through constructing a formal proof that the sum of interior angles in triangle \( \triangle ABC \) equals 180°. ---
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