McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 5.5, Problem 17WE

To determine

To find: The values of x and y .

Expert Solution & Answer

Answer to Problem 17WE

The values of x and y are 9 and 15 respectively.

Explanation of Solution

Given:

The triangle is shown below:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 5.5, Problem 17WE

TA=AB=BCTD=DE=EF

AD=x+3BE=x+yCF=36

Calculation:

Consider a triangle TBE ,

AD is the midsegment of the triangle TBE .

According to the midsegment theorem, the length of midsegment is half of base of triangle.

Hence,

AD=BE2x+3=x+y22x+6=x+yx=y−6 ...... (1)

Consider a trapezoid CFDA ,

BC=ABAnd,EF=DE

Thus, BF is the midsegment of the trapezoid CFDA .

According to the midsegment theorem, the length of midsegment is half of sum of parallel sides of trapezoid.

Hence,

BE=AD+CF2AD+CF=2BEx+3+36=2(x+y)x+39=2x+2yx=39−2y ...... (2)

Solve equations (1) and (2) as follows:

y−6=39−2y3y=45y=15

Substitute 15 for y in equation (1) as follows:

x=15−6=9

Thus, the values of x and y are 9 and 15 respectively.

Chapter 5.5, Problem 16WE

Chapter 5.5, Problem 18WE

Chapter 5 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 5.1 - Prob. 1CE Ch. 5.1 - Prob. 2CE Ch. 5.1 - Prob. 3CE Ch. 5.1 - Prob. 4CE Ch. 5.1 - Prob. 5CE Ch. 5.1 - Prob. 6CE Ch. 5.1 - Prob. 7CE Ch. 5.1 - Prob. 8CE Ch. 5.1 - Prob. 9CE Ch. 5.1 - Prob. 10CE

Ch. 5.1 - Prob. 11CE Ch. 5.1 - Prob. 12CE Ch. 5.1 - Prob. 13CE Ch. 5.1 - Prob. 14CE Ch. 5.1 - Prob. 15CE Ch. 5.1 - Prob. 16CE Ch. 5.1 - Prob. 17CE Ch. 5.1 - Prob. 18CE Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 5WE Ch. 5.1 - Prob. 6WE Ch. 5.1 - Prob. 7WE Ch. 5.1 - Prob. 8WE Ch. 5.1 - Prob. 9WE Ch. 5.1 - Prob. 10WE Ch. 5.1 - Prob. 11WE Ch. 5.1 - Prob. 12WE Ch. 5.1 - Prob. 13WE Ch. 5.1 - Prob. 14WE Ch. 5.1 - Prob. 15WE Ch. 5.1 - Prob. 16WE Ch. 5.1 - Prob. 17WE Ch. 5.1 - Prob. 18WE Ch. 5.1 - Prob. 19WE Ch. 5.1 - Prob. 20WE Ch. 5.1 - Prob. 21WE Ch. 5.1 - Prob. 22WE Ch. 5.1 - Prob. 23WE Ch. 5.1 - Prob. 24WE Ch. 5.1 - Prob. 25WE Ch. 5.1 - Prob. 26WE Ch. 5.1 - Prob. 27WE Ch. 5.1 - Prob. 28WE Ch. 5.1 - Prob. 29WE Ch. 5.1 - Prob. 30WE Ch. 5.1 - Prob. 31WE Ch. 5.1 - Prob. 32WE Ch. 5.1 - Prob. 33WE Ch. 5.1 - Prob. 34WE Ch. 5.1 - Prob. 35WE Ch. 5.1 - Prob. 36WE Ch. 5.1 - Prob. 37WE Ch. 5.1 - Prob. 38WE Ch. 5.1 - Prob. 39WE Ch. 5.2 - Prob. 1CE Ch. 5.2 - Prob. 2CE Ch. 5.2 - Prob. 3CE Ch. 5.2 - Prob. 4CE Ch. 5.2 - Prob. 5CE Ch. 5.2 - Prob. 6CE Ch. 5.2 - Prob. 7CE Ch. 5.2 - Prob. 8CE Ch. 5.2 - Prob. 9CE Ch. 5.2 - Prob. 10CE Ch. 5.2 - Prob. 11CE Ch. 5.2 - Prob. 12CE Ch. 5.2 - Prob. 13CE Ch. 5.2 - Prob. 1WE Ch. 5.2 - Prob. 2WE Ch. 5.2 - Prob. 3WE Ch. 5.2 - Prob. 4WE Ch. 5.2 - Prob. 5WE Ch. 5.2 - Prob. 6WE Ch. 5.2 - Prob. 7WE Ch. 5.2 - Prob. 8WE Ch. 5.2 - Prob. 9WE Ch. 5.2 - Prob. 10WE Ch. 5.2 - Prob. 11WE Ch. 5.2 - Prob. 12WE Ch. 5.2 - Prob. 13WE Ch. 5.2 - Prob. 14WE Ch. 5.2 - Prob. 15WE Ch. 5.2 - Prob. 16WE Ch. 5.2 - Prob. 17WE Ch. 5.2 - Prob. 18WE Ch. 5.2 - Prob. 19WE Ch. 5.2 - Prob. 20WE Ch. 5.2 - Prob. 21WE Ch. 5.2 - Prob. 22WE Ch. 5.2 - Prob. 23WE Ch. 5.2 - Prob. 24WE Ch. 5.2 - Prob. 25WE Ch. 5.3 - Prob. 1CE Ch. 5.3 - Prob. 2CE Ch. 5.3 - Prob. 3CE Ch. 5.3 - Prob. 4CE Ch. 5.3 - Prob. 5CE Ch. 5.3 - Prob. 6CE Ch. 5.3 - Prob. 7CE Ch. 5.3 - Prob. 8CE Ch. 5.3 - Prob. 9CE Ch. 5.3 - Prob. 1WE Ch. 5.3 - Prob. 2WE Ch. 5.3 - Prob. 3WE Ch. 5.3 - Prob. 4WE Ch. 5.3 - Prob. 5WE Ch. 5.3 - Prob. 6WE Ch. 5.3 - Prob. 7WE Ch. 5.3 - Prob. 8WE Ch. 5.3 - Prob. 9WE Ch. 5.3 - Prob. 10WE Ch. 5.3 - Prob. 11WE Ch. 5.3 - Prob. 12WE Ch. 5.3 - Prob. 13WE Ch. 5.3 - Prob. 14WE Ch. 5.3 - Prob. 15WE Ch. 5.3 - Prob. 16WE Ch. 5.3 - Prob. 17WE Ch. 5.3 - Prob. 18WE Ch. 5.3 - Prob. 19WE Ch. 5.3 - Prob. 20WE Ch. 5.3 - Prob. 21WE Ch. 5.3 - Prob. 22WE Ch. 5.3 - Prob. 23WE Ch. 5.3 - Prob. 24WE Ch. 5.3 - Prob. 25WE Ch. 5.3 - Prob. 1ST1 Ch. 5.3 - Prob. 2ST1 Ch. 5.3 - Prob. 3ST1 Ch. 5.3 - Prob. 4ST1 Ch. 5.3 - Prob. 5ST1 Ch. 5.3 - Prob. 6ST1 Ch. 5.3 - Prob. 7ST1 Ch. 5.3 - Prob. 8ST1 Ch. 5.3 - Prob. 1E Ch. 5.3 - Prob. 2E Ch. 5.3 - Prob. 3E Ch. 5.3 - Prob. 4E Ch. 5.3 - Prob. 5E Ch. 5.3 - Prob. 6E Ch. 5.4 - Prob. 1CE Ch. 5.4 - Prob. 2CE Ch. 5.4 - Prob. 3CE Ch. 5.4 - Prob. 4CE Ch. 5.4 - Prob. 5CE Ch. 5.4 - Prob. 6CE Ch. 5.4 - Prob. 7CE Ch. 5.4 - Prob. 8CE Ch. 5.4 - Prob. 9CE Ch. 5.4 - Prob. 10CE Ch. 5.4 - Prob. 11CE Ch. 5.4 - Prob. 1WE Ch. 5.4 - Prob. 2WE Ch. 5.4 - 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Prob. 9MRE Ch. 5.5 - Prob. 1CE Ch. 5.5 - Prob. 2CE Ch. 5.5 - Prob. 3CE Ch. 5.5 - Prob. 4CE Ch. 5.5 - Prob. 5CE Ch. 5.5 - Prob. 6CE Ch. 5.5 - Prob. 7CE Ch. 5.5 - Prob. 8CE Ch. 5.5 - Prob. 9CE Ch. 5.5 - Prob. 10CE Ch. 5.5 - Prob. 11CE Ch. 5.5 - Prob. 1WE Ch. 5.5 - Prob. 2WE Ch. 5.5 - Prob. 3WE Ch. 5.5 - Prob. 4WE Ch. 5.5 - Prob. 5WE Ch. 5.5 - Prob. 6WE Ch. 5.5 - Prob. 7WE Ch. 5.5 - Prob. 8WE Ch. 5.5 - Prob. 9WE Ch. 5.5 - Prob. 10WE Ch. 5.5 - Prob. 11WE Ch. 5.5 - Prob. 12WE Ch. 5.5 - Prob. 13WE Ch. 5.5 - Prob. 14WE Ch. 5.5 - Prob. 15WE Ch. 5.5 - Prob. 16WE Ch. 5.5 - Prob. 17WE Ch. 5.5 - Prob. 18WE Ch. 5.5 - Prob. 19WE Ch. 5.5 - Prob. 20WE Ch. 5.5 - Prob. 21WE Ch. 5.5 - Prob. 22WE Ch. 5.5 - Prob. 23WE Ch. 5.5 - Prob. 24WE Ch. 5.5 - Prob. 25WE Ch. 5.5 - Prob. 26WE Ch. 5.5 - Prob. 27WE Ch. 5.5 - Prob. 28WE Ch. 5.5 - Prob. 29WE Ch. 5.5 - Prob. 30WE Ch. 5.5 - Prob. 31WE Ch. 5.5 - Prob. 32WE Ch. 5.5 - Prob. 33WE Ch. 5.5 - Prob. 34WE Ch. 5.5 - Prob. 35WE Ch. 5.5 - Prob. 36WE Ch. 5.5 - Prob. 1ST2 Ch. 5.5 - Prob. 2ST2 Ch. 5.5 - Prob. 3ST2 Ch. 5.5 - Prob. 4ST2 Ch. 5.5 - Prob. 5ST2 Ch. 5.5 - Prob. 6ST2 Ch. 5.5 - Prob. 7ST2 Ch. 5.5 - Prob. 8ST2 Ch. 5 - Prob. 1CR Ch. 5 - Prob. 2CR Ch. 5 - Prob. 3CR Ch. 5 - Prob. 4CR Ch. 5 - Prob. 5CR Ch. 5 - Prob. 6CR Ch. 5 - Prob. 7CR Ch. 5 - Prob. 8CR Ch. 5 - Prob. 9CR Ch. 5 - Prob. 10CR Ch. 5 - Prob. 11CR Ch. 5 - Prob. 12CR Ch. 5 - Prob. 13CR Ch. 5 - Prob. 14CR Ch. 5 - Prob. 15CR Ch. 5 - Prob. 16CR Ch. 5 - Prob. 17CR Ch. 5 - Prob. 18CR Ch. 5 - Prob. 19CR Ch. 5 - Prob. 20CR Ch. 5 - Prob. 21CR Ch. 5 - Prob. 22CR Ch. 5 - Prob. 1CT Ch. 5 - Prob. 2CT Ch. 5 - Prob. 3CT Ch. 5 - Prob. 4CT Ch. 5 - Prob. 5CT Ch. 5 - Prob. 6CT Ch. 5 - Prob. 7CT Ch. 5 - Prob. 8CT Ch. 5 - Prob. 9CT Ch. 5 - Prob. 10CT Ch. 5 - Prob. 11CT Ch. 5 - Prob. 12CT Ch. 5 - Prob. 13CT Ch. 5 - Prob. 14CT Ch. 5 - Prob. 15CT Ch. 5 - Prob. 16CT Ch. 5 - Prob. 17CT Ch. 5 - Prob. 18CT Ch. 5 - Prob. 19CT Ch. 5 - Prob. 1CUR Ch. 5 - Prob. 2CUR Ch. 5 - Prob. 3CUR Ch. 5 - Prob. 4CUR Ch. 5 - Prob. 5CUR Ch. 5 - 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