The text explains a property of the medians of a triangle:"The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side."**Part B**The diagram shows a triangle labeled \( \triangle ABC \) with medians \( BQ \), \( CR \), and \( AS \). In the given triangle, if \( BP = 8 \, \text{cm} \), determine the length of \( BQ \).**Explanation of Diagram:**The triangle is labeled with vertices \( A \), \( B \), and \( C \). The medians intersect at a point marked as \( P \), which is the centroid. The question relates the length of the segment \( BP \) to \( BQ \) since the centroid divides each median into a ratio of 2:1.**Calculation Required:**Using the property of the centroid, since \( BP = 8 \, \text{cm} \), \( BQ \) is two-thirds of the entire median \( BQ \).

Topic - Triangles We are given BP=8 cmand we need to find BQWe know thatThe medians of a triangle are concurrent at a point that two-thirds the distancefrom each vertex to the mid point of the opposite side.BP=23BQ,BQ=32BP=32×8=12 cmThe length of BQ=12 cm

Math

Geometry

The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. Part B In the following diagram, BQ, CR and AS are the medians of the triangle ABC. If BP=8 cm, the length of BQ is | cm.

The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. Part B In the following diagram, BQ, CR and AS are the medians of the triangle ABC. If BP=8 cm, the length of BQ is | cm.

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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Question

The text explains a property of the medians of a triangle:

"The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side."

**Part B**

The diagram shows a triangle labeled \( \triangle ABC \) with medians \( BQ \), \( CR \), and \( AS \). In the given triangle, if \( BP = 8 \, \text{cm} \), determine the length of \( BQ \).

**Explanation of Diagram:**
The triangle is labeled with vertices \( A \), \( B \), and \( C \). The medians intersect at a point marked as \( P \), which is the centroid. The question relates the length of the segment \( BP \) to \( BQ \) since the centroid divides each median into a ratio of 2:1.

**Calculation Required:**
Using the property of the centroid, since \( BP = 8 \, \text{cm} \), \( BQ \) is two-thirds of the entire median \( BQ \).

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