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Z is the centroid of AUVW. Zis the intersection of the triangle's A. medians O B. altitudes C. angle bisectors O D. perpendicular bisectors

Z is the centroid of AUVW. Zis the intersection of the triangle's A. medians O B. altitudes C. angle bisectors O D. perpendicular bisectors

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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### Understanding the Centroid of a Triangle In the following diagram, point \( Z \) is identified as the centroid of triangle \( \triangle UVW \). #### Diagram Explanation: - The triangle \( \triangle UVW \) is depicted with vertices labeled \( U \), \( V \), and \( W \). - Inside the triangle, point \( Z \) is marked as the centroid. - Three segments are shown: - Segment \( UW \) - Segment \( WV \) - Segment \( UV \) - Medians of the triangle (segments from each vertex to the midpoint of the opposite side) intersect at point \( Z \). The centroid (point \( Z \)) of a triangle is the point where all three medians intersect. It is also known as the "center of mass" and is located at a position where it balances the triangle. ### Question: Which of the following geometric constructs intersect at the centroid \( Z \) of the triangle \( \triangle UVW \)? A. Medians B. Altitudes C. Angle Bisectors D. Perpendicular Bisectors ### Options: - **A** - Medians: The correct answer. The centroid is the intersection point of the medians of the triangle. - **B** - Altitudes: These are segments from each vertex perpendicular to the opposite side, intersecting at the orthocenter. - **C** - Angle Bisectors: These intersect at the incenter, which is the center of the inscribed circle. - **D** - Perpendicular Bisectors: These intersect at the circumcenter, which is the center of the circumscribed circle. #### Select the correct option to check your understanding of the geometrical properties of the centroid.
Transcribed Image Text:### Understanding the Centroid of a Triangle In the following diagram, point \( Z \) is identified as the centroid of triangle \( \triangle UVW \). #### Diagram Explanation: - The triangle \( \triangle UVW \) is depicted with vertices labeled \( U \), \( V \), and \( W \). - Inside the triangle, point \( Z \) is marked as the centroid. - Three segments are shown: - Segment \( UW \) - Segment \( WV \) - Segment \( UV \) - Medians of the triangle (segments from each vertex to the midpoint of the opposite side) intersect at point \( Z \). The centroid (point \( Z \)) of a triangle is the point where all three medians intersect. It is also known as the "center of mass" and is located at a position where it balances the triangle. ### Question: Which of the following geometric constructs intersect at the centroid \( Z \) of the triangle \( \triangle UVW \)? A. Medians B. Altitudes C. Angle Bisectors D. Perpendicular Bisectors ### Options: - **A** - Medians: The correct answer. The centroid is the intersection point of the medians of the triangle. - **B** - Altitudes: These are segments from each vertex perpendicular to the opposite side, intersecting at the orthocenter. - **C** - Angle Bisectors: These intersect at the incenter, which is the center of the inscribed circle. - **D** - Perpendicular Bisectors: These intersect at the circumcenter, which is the center of the circumscribed circle. #### Select the correct option to check your understanding of the geometrical properties of the centroid.
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