Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Chapter 7.3, Problem 31E
Given: Regular pentagon RSTVQ with equilateral
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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side FG. Round your answer to the nearest tenth if necessary.
BCDEFGHI2737.55
Chapter 7 Solutions
Elementary Geometry for College Students
Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 3ECh. 7.1 - In Exercises 3 to 8, use the drawing provided....Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...
Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 12ECh. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - In Exercises 39 and 42, refer to the line segments...Ch. 7.1 - Prob. 44ECh. 7.1 - In Exercises 39 and 42, refer to the line segments...Ch. 7.1 - Prob. 46ECh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - What is the general name of the point of...Ch. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Which lines or line segments or rays must be drawn...Ch. 7.2 - Is it really necessary to construct all three...Ch. 7.2 - Prob. 9ECh. 7.2 - a To locate the orthocenter, is it necessary to...Ch. 7.2 - To locate the centroid of a triangle, is it...Ch. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Must the centroid of an isosceles triangle lie on...Ch. 7.2 - Draw a triangle and, by construction, find its...Ch. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Draw an obtuse triangle and, by construction, find...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Is the incenter always located in the interior of...Ch. 7.2 - Prob. 23ECh. 7.2 - Find the length of the radius of the inscribed...Ch. 7.2 - Find the distance from the circumcenter to each...Ch. 7.2 - A triangle has angles measuring 30, 30, and 120....Ch. 7.2 - Given: Isosceles RST RS=RT=17andST=16. Medians RZ,...Ch. 7.2 - Given: Isosceles RST RS=RT=10andST=16. Medians RZ,...Ch. 7.2 - In MNP, medians MB, NA and PC intersect at...Ch. 7.2 - In MNP for Exercise 29, medians MB, NA and PC...Ch. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Does a rectangle have a an incenter? b a...Ch. 7.2 - Does a square have a an incenter? b a...Ch. 7.2 - Prob. 36ECh. 7.2 - Does a rhombus have a an incenter? b a...Ch. 7.2 - Does a isosceles trapezoid have a an incenter?.b a...Ch. 7.2 - A distributing company plans an Illinois location...Ch. 7.2 - There are plans to locate a disaster response...Ch. 7.2 - A circle is inscribed in an isosceles triangle...Ch. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.3 - Describe, if possible, how you would inscribe a...Ch. 7.3 - What condition must be satisfied for it to be...Ch. 7.3 - Prob. 3ECh. 7.3 - What condition must be satisfied for it to be...Ch. 7.3 - Prob. 5ECh. 7.3 - In Exercises 5 to 8, perform constructions....Ch. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Find the perimeter of a regular octagon if the...Ch. 7.3 - In a regular polygon with each side of length 6.5...Ch. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Find the lengths of the apothem and the radius of...Ch. 7.3 - Find the lengths of the apothem and the radius of...Ch. 7.3 - Prob. 15ECh. 7.3 - Find the lengths of the side and the radius of a...Ch. 7.3 - Find the measure of a central angle of a regular...Ch. 7.3 - Find the measure of a central angle of a regular...Ch. 7.3 - Find the number of sides of a regular polygon that...Ch. 7.3 - Find the number of sides of a regular polygon that...Ch. 7.3 - Find the measure of each interior angle of a...Ch. 7.3 - Find the measure of each interior angle of a...Ch. 7.3 - Prob. 23ECh. 7.3 - Find the measure of each exterior angle of a...Ch. 7.3 - Find the number of sides for a regular polygon in...Ch. 7.3 - Find the number of sides for a regular polygon in...Ch. 7.3 - Is there a regular polygon for which each central...Ch. 7.3 - Given regular hexagon ABCDEF with each side of...Ch. 7.3 - Given regular octagon RSTUVWXY with each side of...Ch. 7.3 - Given that RSTVQ is a regular pentagon and PQR is...Ch. 7.3 - Given: Regular pentagon RSTVQ with equilateral ...Ch. 7.3 - Given: Regular pentagon JKLMN not shown with...Ch. 7.3 - Is there a regular polygon with 8 diagonals? If...Ch. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Find the measure of a central angle of a regular...Ch. 7.CR - In Review Exercises 1 to 6, use the figure shown....Ch. 7.CR - Prob. 2CRCh. 7.CR - In Review Exercises 1 to 6, use the figure shown....Ch. 7.CR - Prob. 4CRCh. 7.CR - Prob. 5CRCh. 7.CR - Prob. 6CRCh. 7.CR - Prob. 7CRCh. 7.CR - Prob. 8CRCh. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - Prob. 11CRCh. 7.CR - Prob. 12CRCh. 7.CR - Prob. 13CRCh. 7.CR - Prob. 14CRCh. 7.CR - Prob. 15CRCh. 7.CR - Prob. 16CRCh. 7.CR - Prob. 17CRCh. 7.CR - Prob. 18CRCh. 7.CR - Prob. 19CRCh. 7.CR - Prob. 20CRCh. 7.CR - Prob. 21CRCh. 7.CR - Prob. 22CRCh. 7.CR - Prob. 23CRCh. 7.CR - Prob. 24CRCh. 7.CR - Prob. 25CRCh. 7.CR - Prob. 26CRCh. 7.CR - Prob. 27CRCh. 7.CR - In a regular polygon, each central angle measures...Ch. 7.CR - Prob. 29CRCh. 7.CR - Prob. 30CRCh. 7.CR - Can a circle be inscribed in each of the following...Ch. 7.CR - The length of the radius of a circle inscribed in...Ch. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CT - Draw and describe the locus of points in the plane...Ch. 7.CT - Prob. 2CTCh. 7.CT - Prob. 3CTCh. 7.CT - Prob. 4CTCh. 7.CT - Describe the locus of points in space that are at...Ch. 7.CT - Prob. 6CTCh. 7.CT - For a given triangle such as ABC, what word...Ch. 7.CT - Prob. 8CTCh. 7.CT - Which of the following must be concurrent at an...Ch. 7.CT - Classify as true/false: aA circle can be inscribed...Ch. 7.CT - Prob. 11CTCh. 7.CT - Prob. 12CTCh. 7.CT - Prob. 13CTCh. 7.CT - For a regular octagon, the length of the apothem...Ch. 7.CT - For a regular hexagon ABCDEF, the length of side...Ch. 7.CT - For rectangle MNPQ, points A, B, C and D are the...Ch. 7.CT - Prob. 17CT
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