a) Answer Theorem 5.4 is converse of theorem 5.1, that states that If both pairs of opposite sides of a quadrilateral are congruent, then quadrilateral is a parallelogram.” Explanation Given information: Statements of following theorem is given, Theorem 5.1: “Opposite sides of a parallelogram are congruent.’ Concept used : Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem. Calculation: On observing different sections given, it is found that the converse to theorem 5.1 is theorem 5.4 that’s statement is, “If both pairs of opposite sides of a quadrilateral are congruent, then quadrilateral is a parallelogram.” Conclusion : Thus, theorem 5.4 is the converse of given theorem 5.1. b) To determine To find: The theorem that is converse to said theorems 5.2. Answer Theorem 5.6 is converse of theorem 5.2, that states that If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.” Explanation Given information: Statements of following theorems are given, Theorem 5.2: “Opposite angles of a parallelogram are congruent.” Concept used : Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem. Calculation: On observing different sections given, it is found that the converse to theorem 5.2 is theorem 5.6 that’s statement is, “If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.” Conclusion : Thus, theorem 5.6 is the converse of given theorem 5.2. c) To determine To find: The theorem that is converse to said theorems 5.3. Answer Theorem 5.7 is converse of theorem 5.3, that states that “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.” Explanation Given information: Statements of following theorems are given, Theorem 5.3: ”Diagonals of a parallelogram bisect each other.” Concept used : Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem. Calculation: On observing different sections given, it is found that the converse to theorem 5.3 is theorem 5.7 that’s statement is, “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.” Conclusion : Thus, theorem 5.7 is the converse of given theorem 5.3. a) To determine To find: The theorems that are converse to said theorems 5.1,5.2 and 5.3. Answer Theorem 5.4 is converse of theorem 5.1, theorem 5.6 is converse of theorem 5.2 and theorem 5.7 is converse of theorem 5.3. Explanation Given information: Statements of following theorems are given, Theorem 5.1: “Opposite sides of a parallelogram are congruent.’ Theorem 5.2: “Opposite angles of a parallelogram are congruent.” Theorem 5.3: ”Diagonals of a parallelogram bisect each other.” Concept used : Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem. Calculation: On observing different sections given, it is found that the converse to theorem 5.1 is theorem 5.4 that’s statement is, “If both pairs of opposite sides of a quadrilateral are congruent, then quadrilateral is a parallelogram.” Converse to theorem 5.2 is theorem 5.6 that’s statement is, “If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.” Converse to theorem 5.3 is theorem 5.7 that’s statement is, “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.” Conclusion : Thus, theorem 5.4, theorem 5.6 and theorem 5.7 are the converse of given theorems.

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

Chapter 5.2, Problem 9WE

To determine

To find: The theorem that is converse to said theorems 5.1.

Expert Solution

Answer to Problem 9WE

Theorem 5.4 is converse of theorem 5.1, that states that If both pairs of opposite sides of a quadrilateral are congruent, then quadrilateral is a parallelogram.”

Explanation of Solution

Given information: Statements of following theorem is given,

Theorem 5.1: “Opposite sides of a parallelogram are congruent.’

Concept used: Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem.

Calculation: On observing different sections given, it is found that the converse to theorem 5.1 is theorem 5.4 that’s statement is, “If both pairs of opposite sides of a quadrilateral are congruent, then quadrilateral is a parallelogram.”

Conclusion: Thus, theorem 5.4 is the converse of given theorem 5.1.

To determine

To find: The theorem that is converse to said theorems 5.2.

Expert Solution

Answer to Problem 9WE

Theorem 5.6 is converse of theorem 5.2, that states that If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.”

Explanation of Solution

Given information: Statements of following theorems are given,

Theorem 5.2: “Opposite angles of a parallelogram are congruent.”

Concept used: Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem.

Calculation: On observing different sections given, it is found that the converse to theorem 5.2 is theorem 5.6 that’s statement is, “If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.”

Conclusion: Thus, theorem 5.6 is the converse of given theorem 5.2.

To determine

To find: The theorem that is converse to said theorems 5.3.

Expert Solution

Answer to Problem 9WE

Theorem 5.7 is converse of theorem 5.3, that states that “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.”

Explanation of Solution

Given information: Statements of following theorems are given,

Theorem 5.3: ”Diagonals of a parallelogram bisect each other.”

Concept used: Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem.

Calculation: On observing different sections given, it is found that the converse to theorem 5.3 is theorem 5.7 that’s statement is, “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.”

Conclusion: Thus, theorem 5.7 is the converse of given theorem 5.3.

To determine

To find: The theorems that are converse to said theorems 5.1,5.2 and 5.3.

Expert Solution

Answer to Problem 9WE

Theorem 5.4 is converse of theorem 5.1, theorem 5.6 is converse of theorem 5.2 and theorem 5.7 is converse of theorem 5.3.

Explanation of Solution

Given information: Statements of following theorems are given,

Theorem 5.1: “Opposite sides of a parallelogram are congruent.’

Theorem 5.2: “Opposite angles of a parallelogram are congruent.”

Theorem 5.3: ”Diagonals of a parallelogram bisect each other.”

Concept used: Converse of a theorem is a statement that is formed by interchanging the given section of a theorem by what to prove and what to prove section by given section of the theorem.

Converse to theorem 5.2 is theorem 5.6 that’s statement is, “If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.”

Converse to theorem 5.3 is theorem 5.7 that’s statement is, “If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.”

Conclusion: Thus, theorem 5.4, theorem 5.6 and theorem 5.7 are the converse of given theorems.

Chapter 5.2, Problem 8WE

Chapter 5.2, Problem 10WE

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 - Prob. 3WE Ch. 5.4 - Prob. 4WE Ch. 5.4 - Prob. 5WE Ch. 5.4 - Prob. 6WE Ch. 5.4 - Prob. 7WE Ch. 5.4 - Prob. 8WE Ch. 5.4 - Prob. 9WE Ch. 5.4 - Prob. 10WE Ch. 5.4 - Prob. 11WE Ch. 5.4 - Prob. 12WE Ch. 5.4 - Prob. 13WE Ch. 5.4 - Prob. 14WE Ch. 5.4 - Prob. 15WE Ch. 5.4 - Prob. 16WE Ch. 5.4 - Prob. 17WE Ch. 5.4 - Prob. 18WE Ch. 5.4 - Prob. 19WE Ch. 5.4 - Prob. 20WE Ch. 5.4 - Prob. 21WE Ch. 5.4 - Prob. 22WE Ch. 5.4 - Prob. 23WE Ch. 5.4 - Prob. 24WE Ch. 5.4 - Prob. 25WE Ch. 5.4 - Prob. 26WE Ch. 5.4 - Prob. 27WE Ch. 5.4 - Prob. 28WE Ch. 5.4 - Prob. 29WE Ch. 5.4 - Prob. 30WE Ch. 5.4 - Prob. 31WE Ch. 5.4 - Prob. 32WE Ch. 5.4 - Prob. 33WE Ch. 5.4 - Prob. 34WE Ch. 5.4 - Prob. 35WE Ch. 5.4 - Prob. 36WE Ch. 5.4 - Prob. 37WE Ch. 5.4 - Prob. 38WE Ch. 5.4 - Prob. 39WE Ch. 5.4 - Prob. 40WE Ch. 5.4 - Prob. 41WE Ch. 5.4 - Prob. 42WE Ch. 5.4 - Prob. 1MRE Ch. 5.4 - Prob. 2MRE Ch. 5.4 - Prob. 3MRE Ch. 5.4 - Prob. 4MRE Ch. 5.4 - Prob. 5MRE Ch. 5.4 - Prob. 6MRE Ch. 5.4 - Prob. 7MRE Ch. 5.4 - Prob. 8MRE Ch. 5.4 - 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 - Prob. 6CUR Ch. 5 - Prob. 7CUR Ch. 5 - Prob. 8CUR Ch. 5 - Prob. 9CUR Ch. 5 - Prob. 10CUR Ch. 5 - Prob. 11CUR Ch. 5 - Prob. 12CUR Ch. 5 - Prob. 13CUR Ch. 5 - Prob. 14CUR Ch. 5 - Prob. 15CUR Ch. 5 - Prob. 16CUR Ch. 5 - Prob. 17CUR Ch. 5 - Prob. 18CUR Ch. 5 - Prob. 19CUR Ch. 5 - Prob. 20CUR Ch. 5 - Prob. 21CUR Ch. 5 - Prob. 22CUR Ch. 5 - Prob. 23CUR Ch. 5 - Prob. 24CUR Ch. 5 - Prob. 25CUR Ch. 5 - Prob. 26CUR Ch. 5 - Prob. 27CUR Ch. 5 - Prob. 28CUR Ch. 5 - Prob. 29CUR Ch. 5 - Prob. 30CUR Ch. 5 - Prob. 31CUR

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