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High School Math Geometry Geometry, Student Edition

To prove: m ∠ A = 1 2 ( m D E − m B C )

To prove: m ∠ A = 1 2 ( m D E − m B C )

Geometry, Student Edition

Geometry, Student Edition

1st Edition

ISBN: 9780078884849

Author: McGraw-Hill, McGraw Hill

Publisher: Glencoe/McGraw-Hill School Pub Co

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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 10.6, Problem 30PPS

To determine

To prove: m∠A=12(mDE−mBC)

Expert Solution & Answer

Explanation of Solution

Given:

The given figure is

Geometry, Student Edition, Chapter 10.6, Problem 30PPS

Calculation:

Angle DCE is the exterior angle of the triangle ADC therefore,

∠DCE=∠DAC+∠ADC

Angle DCE and angle BDC is inscribed by the arc DE and BC, therefore,

m∠DCE=12mDEandm∠BDC=m∠ADC=12mBC

Therefore,

12mDE=m∠DAC+12mBCm∠DAC=12mBC−12mDEm∠A=12(mDE−mBC)

Chapter 10.6, Problem 29PPS

Chapter 10.6, Problem 31PPS

Chapter 10 Solutions

Geometry, Student Edition

Ch. 10.1 - Prob. 1CYP Ch. 10.1 - Prob. 2ACYP Ch. 10.1 - Prob. 2BCYP Ch. 10.1 - Prob. 3CYP Ch. 10.1 - Prob. 4ACYP Ch. 10.1 - Prob. 4BCYP Ch. 10.1 - Prob. 5CYP Ch. 10.1 - Prob. 6ACYP Ch. 10.1 - Prob. 6BCYP Ch. 10.1 - Prob. 1CYU

Ch. 10.1 - Prob. 2CYU Ch. 10.1 - Prob. 3CYU Ch. 10.1 - Prob. 4CYU Ch. 10.1 - Prob. 5CYU Ch. 10.1 - Prob. 6CYU Ch. 10.1 - Prob. 7CYU Ch. 10.1 - Prob. 8CYU Ch. 10.1 - Prob. 9CYU Ch. 10.1 - Prob. 10PPS Ch. 10.1 - Prob. 11PPS Ch. 10.1 - Prob. 12PPS Ch. 10.1 - Prob. 13PPS Ch. 10.1 - Prob. 14PPS Ch. 10.1 - Prob. 15PPS Ch. 10.1 - Prob. 16PPS Ch. 10.1 - Prob. 17PPS Ch. 10.1 - Prob. 18PPS Ch. 10.1 - Prob. 19PPS Ch. 10.1 - Prob. 20PPS Ch. 10.1 - Prob. 21PPS Ch. 10.1 - Prob. 22PPS Ch. 10.1 - Prob. 23PPS Ch. 10.1 - Prob. 24PPS Ch. 10.1 - Prob. 25PPS Ch. 10.1 - Prob. 26PPS Ch. 10.1 - Prob. 27PPS Ch. 10.1 - Prob. 28PPS Ch. 10.1 - Prob. 29PPS Ch. 10.1 - Prob. 30PPS Ch. 10.1 - Prob. 31PPS Ch. 10.1 - Prob. 32PPS Ch. 10.1 - Prob. 33PPS Ch. 10.1 - Prob. 34PPS Ch. 10.1 - Prob. 35PPS Ch. 10.1 - Prob. 36PPS Ch. 10.1 - Prob. 37PPS Ch. 10.1 - Prob. 38PPS Ch. 10.1 - Prob. 39PPS Ch. 10.1 - Prob. 40PPS Ch. 10.1 - Prob. 41PPS Ch. 10.1 - Prob. 42PPS Ch. 10.1 - Prob. 43PPS Ch. 10.1 - Prob. 44PPS Ch. 10.1 - Prob. 45PPS Ch. 10.1 - Prob. 46PPS Ch. 10.1 - Prob. 47PPS Ch. 10.1 - Prob. 48HP Ch. 10.1 - Prob. 49HP Ch. 10.1 - Prob. 50HP Ch. 10.1 - Prob. 51HP Ch. 10.1 - Prob. 52HP Ch. 10.1 - Prob. 53HP Ch. 10.1 - Prob. 54HP Ch. 10.1 - Prob. 55STP Ch. 10.1 - Prob. 56STP Ch. 10.1 - Prob. 57STP Ch. 10.1 - Prob. 58STP Ch. 10.1 - Prob. 59SPR Ch. 10.1 - Prob. 60SPR Ch. 10.1 - Prob. 61SPR Ch. 10.1 - Prob. 62SPR Ch. 10.1 - Prob. 63SPR Ch. 10.1 - Prob. 64SPR Ch. 10.1 - Prob. 65SPR Ch. 10.1 - Prob. 66SPR Ch. 10.1 - Prob. 67SPR Ch. 10.1 - Prob. 68SPR Ch. 10.1 - Prob. 69SR Ch. 10.1 - Prob. 70SR Ch. 10.1 - Prob. 71SR Ch. 10.1 - Prob. 72SR Ch. 10.2 - Prob. 1ACYP Ch. 10.2 - Prob. 1BCYP Ch. 10.2 - Prob. 2ACYP Ch. 10.2 - Prob. 2BCYP Ch. 10.2 - Prob. 2CCYP Ch. 10.2 - Prob. 3ACYP Ch. 10.2 - Prob. 3BCYP Ch. 10.2 - Prob. 4ACYP Ch. 10.2 - Prob. 4BCYP Ch. 10.2 - Prob. 5ACYP Ch. 10.2 - Prob. 5BCYP Ch. 10.2 - Prob. 5CCYP Ch. 10.2 - Prob. 1CYU Ch. 10.2 - Prob. 2CYU Ch. 10.2 - Prob. 3CYU Ch. 10.2 - Prob. 4CYU Ch. 10.2 - Prob. 5CYU Ch. 10.2 - Prob. 6CYU Ch. 10.2 - Prob. 7CYU Ch. 10.2 - Prob. 8CYU Ch. 10.2 - Prob. 9CYU Ch. 10.2 - Prob. 10CYU Ch. 10.2 - Prob. 11CYU Ch. 10.2 - Prob. 12PPS Ch. 10.2 - Prob. 13PPS Ch. 10.2 - Prob. 14PPS Ch. 10.2 - Prob. 15PPS Ch. 10.2 - Prob. 16PPS Ch. 10.2 - Prob. 17PPS Ch. 10.2 - Prob. 18PPS Ch. 10.2 - Prob. 19PPS Ch. 10.2 - Prob. 20PPS Ch. 10.2 - Prob. 21PPS Ch. 10.2 - Prob. 22PPS Ch. 10.2 - Prob. 23PPS Ch. 10.2 - Prob. 24PPS Ch. 10.2 - Prob. 25PPS Ch. 10.2 - Prob. 26PPS Ch. 10.2 - Prob. 27PPS Ch. 10.2 - Prob. 28PPS Ch. 10.2 - Prob. 29PPS Ch. 10.2 - Prob. 30PPS Ch. 10.2 - Prob. 31PPS Ch. 10.2 - Prob. 32PPS Ch. 10.2 - Prob. 33PPS Ch. 10.2 - Prob. 34PPS Ch. 10.2 - Prob. 35PPS Ch. 10.2 - Prob. 36PPS Ch. 10.2 - Prob. 37PPS Ch. 10.2 - Prob. 38PPS Ch. 10.2 - Prob. 39PPS Ch. 10.2 - Prob. 40PPS Ch. 10.2 - Prob. 41PPS Ch. 10.2 - Prob. 42PPS Ch. 10.2 - Prob. 43PPS Ch. 10.2 - Prob. 44PPS Ch. 10.2 - Prob. 45PPS Ch. 10.2 - Prob. 46PPS Ch. 10.2 - Prob. 47PPS Ch. 10.2 - Prob. 48PPS Ch. 10.2 - Prob. 49PPS Ch. 10.2 - Prob. 50PPS Ch. 10.2 - Prob. 51PPS Ch. 10.2 - Prob. 52PPS Ch. 10.2 - Prob. 53PPS Ch. 10.2 - Prob. 55HP Ch. 10.2 - Prob. 56HP Ch. 10.2 - Prob. 57HP Ch. 10.2 - Prob. 58HP Ch. 10.2 - Prob. 59HP Ch. 10.2 - Prob. 60HP Ch. 10.2 - Prob. 61HP Ch. 10.2 - Prob. 62HP Ch. 10.2 - Prob. 63STP Ch. 10.2 - Prob. 64STP Ch. 10.2 - Prob. 65STP Ch. 10.2 - Prob. 66STP Ch. 10.2 - Prob. 67SPR Ch. 10.2 - Prob. 68SPR Ch. 10.2 - Prob. 69SPR Ch. 10.2 - Prob. 70SPR Ch. 10.2 - Prob. 71SPR Ch. 10.2 - Prob. 72SPR Ch. 10.2 - Prob. 73SPR Ch. 10.2 - Prob. 74SPR Ch. 10.2 - Prob. 75SR Ch. 10.2 - Prob. 76SR Ch. 10.2 - Prob. 77SR Ch. 10.3 - Prob. 1CYP Ch. 10.3 - Prob. 2CYP Ch. 10.3 - Prob. 3CYP Ch. 10.3 - Prob. 4CYP Ch. 10.3 - Prob. 5CYP Ch. 10.3 - Prob. 1CYU Ch. 10.3 - Prob. 2CYU Ch. 10.3 - Prob. 3CYU Ch. 10.3 - Prob. 4CYU Ch. 10.3 - Prob. 5CYU Ch. 10.3 - Prob. 6CYU Ch. 10.3 - Prob. 7PPS Ch. 10.3 - Prob. 8PPS Ch. 10.3 - Prob. 9PPS Ch. 10.3 - Prob. 10PPS Ch. 10.3 - Prob. 11PPS Ch. 10.3 - Prob. 12PPS Ch. 10.3 - Prob. 13PPS Ch. 10.3 - Prob. 14PPS Ch. 10.3 - 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Prob. 1CYU Ch. 10.4 - Prob. 2CYU Ch. 10.4 - Prob. 3CYU Ch. 10.4 - Prob. 4CYU Ch. 10.4 - Prob. 5CYU Ch. 10.4 - Prob. 6CYU Ch. 10.4 - Prob. 7CYU Ch. 10.4 - Prob. 8CYU Ch. 10.4 - Prob. 9CYU Ch. 10.4 - Prob. 10CYU Ch. 10.4 - Prob. 11PPS Ch. 10.4 - Prob. 12PPS Ch. 10.4 - Prob. 13PPS Ch. 10.4 - Prob. 14PPS Ch. 10.4 - Prob. 15PPS Ch. 10.4 - Prob. 16PPS Ch. 10.4 - Prob. 17PPS Ch. 10.4 - Prob. 18PPS Ch. 10.4 - Prob. 19PPS Ch. 10.4 - Prob. 20PPS Ch. 10.4 - Prob. 21PPS Ch. 10.4 - Prob. 22PPS Ch. 10.4 - Prob. 23PPS Ch. 10.4 - Prob. 24PPS Ch. 10.4 - Prob. 25PPS Ch. 10.4 - Prob. 26PPS Ch. 10.4 - Prob. 27PPS Ch. 10.4 - Prob. 28PPS Ch. 10.4 - Prob. 29PPS Ch. 10.4 - Prob. 30PPS Ch. 10.4 - Prob. 31PPS Ch. 10.4 - Prob. 32PPS Ch. 10.4 - Prob. 33PPS Ch. 10.4 - Prob. 34PPS Ch. 10.4 - Prob. 35PPS Ch. 10.4 - Prob. 36PPS Ch. 10.4 - Prob. 37PPS Ch. 10.4 - Prob. 38PPS Ch. 10.4 - Prob. 39PPS Ch. 10.4 - Prob. 40PPS Ch. 10.4 - Prob. 41PPS Ch. 10.4 - Prob. 42HP Ch. 10.4 - Prob. 43HP Ch. 10.4 - Prob. 44HP Ch. 10.4 - Prob. 45HP Ch. 10.4 - Prob. 46HP Ch. 10.4 - Prob. 47HP Ch. 10.4 - Prob. 48HP Ch. 10.4 - Prob. 49HP Ch. 10.4 - Prob. 50HP Ch. 10.4 - Prob. 51STP Ch. 10.4 - Prob. 52STP Ch. 10.4 - Prob. 53STP Ch. 10.4 - Prob. 54STP Ch. 10.4 - Prob. 55SPR Ch. 10.4 - Prob. 56SPR Ch. 10.4 - Prob. 57SPR Ch. 10.4 - Prob. 58SPR Ch. 10.4 - Prob. 59SPR Ch. 10.4 - Prob. 60SPR Ch. 10.4 - Prob. 61SPR Ch. 10.4 - Prob. 62SPR Ch. 10.4 - Prob. 63SR Ch. 10.4 - Prob. 64SR Ch. 10.4 - Prob. 65SR Ch. 10.4 - Prob. 66SR Ch. 10.5 - Prob. 1ACYP Ch. 10.5 - Prob. 1BCYP Ch. 10.5 - Prob. 2CYP Ch. 10.5 - Prob. 3ACYP Ch. 10.5 - Prob. 3BCYP Ch. 10.5 - Prob. 4ACYP Ch. 10.5 - Prob. 4BCYP Ch. 10.5 - Prob. 5CYP Ch. 10.5 - Prob. 1CYU Ch. 10.5 - Prob. 2CYU Ch. 10.5 - Prob. 3CYU Ch. 10.5 - Prob. 4CYU Ch. 10.5 - Prob. 5CYU Ch. 10.5 - Prob. 6CYU Ch. 10.5 - Prob. 7CYU Ch. 10.5 - Prob. 8CYU Ch. 10.5 - Prob. 9PPS Ch. 10.5 - Prob. 10PPS Ch. 10.5 - Prob. 11PPS Ch. 10.5 - Prob. 12PPS Ch. 10.5 - Prob. 13PPS Ch. 10.5 - Prob. 14PPS Ch. 10.5 - Prob. 15PPS Ch. 10.5 - 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Prob. 2BCYP Ch. 10.6 - Prob. 3ACYP Ch. 10.6 - Prob. 3BCYP Ch. 10.6 - Prob. 4CYP Ch. 10.6 - Prob. 1CYU Ch. 10.6 - Prob. 2CYU Ch. 10.6 - Prob. 3CYU Ch. 10.6 - Prob. 4CYU Ch. 10.6 - Prob. 5CYU Ch. 10.6 - Prob. 6CYU Ch. 10.6 - Prob. 7CYU Ch. 10.6 - Prob. 8PPS Ch. 10.6 - Prob. 9PPS Ch. 10.6 - Prob. 10PPS Ch. 10.6 - Prob. 11PPS Ch. 10.6 - Prob. 12PPS Ch. 10.6 - Prob. 13PPS Ch. 10.6 - Prob. 14PPS Ch. 10.6 - Prob. 15PPS Ch. 10.6 - Prob. 16PPS Ch. 10.6 - Prob. 17PPS Ch. 10.6 - Prob. 18PPS Ch. 10.6 - Prob. 19PPS Ch. 10.6 - Prob. 20PPS Ch. 10.6 - Prob. 21PPS Ch. 10.6 - Prob. 22PPS Ch. 10.6 - Prob. 23PPS Ch. 10.6 - Prob. 24PPS Ch. 10.6 - Prob. 25PPS Ch. 10.6 - Prob. 26PPS Ch. 10.6 - Prob. 27PPS Ch. 10.6 - Prob. 28PPS Ch. 10.6 - Prob. 29PPS Ch. 10.6 - Prob. 30PPS Ch. 10.6 - Prob. 31PPS Ch. 10.6 - Prob. 32PPS Ch. 10.6 - Prob. 33PPS Ch. 10.6 - Prob. 34PPS Ch. 10.6 - Prob. 35PPS Ch. 10.6 - Prob. 36HP Ch. 10.6 - Prob. 37HP Ch. 10.6 - Prob. 38HP Ch. 10.6 - Prob. 39HP Ch. 10.6 - Prob. 40HP Ch. 10.6 - Prob. 41HP Ch. 10.6 - Prob. 42STP Ch. 10.6 - Prob. 43STP Ch. 10.6 - Prob. 44STP Ch. 10.6 - Prob. 45STP Ch. 10.6 - Prob. 46SPR Ch. 10.6 - Prob. 47SPR Ch. 10.6 - Prob. 48SPR Ch. 10.6 - Prob. 49SPR Ch. 10.6 - Prob. 50SPR Ch. 10.6 - Prob. 51SPR Ch. 10.6 - Prob. 52SPR Ch. 10.6 - Prob. 53SR Ch. 10.6 - Prob. 54SR Ch. 10.6 - Prob. 55SR Ch. 10.6 - Prob. 56SR Ch. 10.6 - Prob. 57SR Ch. 10.6 - Prob. 58SR Ch. 10.7 - Prob. 1ACYP Ch. 10.7 - Prob. 1BCYP Ch. 10.7 - Prob. 2CYP Ch. 10.7 - Prob. 3ACYP Ch. 10.7 - Prob. 3BCYP Ch. 10.7 - Prob. 4CYP Ch. 10.7 - Prob. 1CYU Ch. 10.7 - Prob. 2CYU Ch. 10.7 - Prob. 3CYU Ch. 10.7 - Prob. 4CYU Ch. 10.7 - Prob. 5CYU Ch. 10.7 - Prob. 6PPS Ch. 10.7 - Prob. 7PPS Ch. 10.7 - Prob. 8PPS Ch. 10.7 - Prob. 9PPS Ch. 10.7 - Prob. 10PPS Ch. 10.7 - Prob. 11PPS Ch. 10.7 - Prob. 12PPS Ch. 10.7 - Prob. 13PPS Ch. 10.7 - Prob. 14PPS Ch. 10.7 - Prob. 15PPS Ch. 10.7 - Prob. 16PPS Ch. 10.7 - Prob. 17PPS Ch. 10.7 - Prob. 18PPS Ch. 10.7 - Prob. 19PPS Ch. 10.7 - Prob. 20PPS Ch. 10.7 - Prob. 21PPS Ch. 10.7 - Prob. 22PPS Ch. 10.7 - Prob. 23PPS Ch. 10.7 - Prob. 24PPS Ch. 10.7 - Prob. 25PPS Ch. 10.7 - Prob. 26HP Ch. 10.7 - Prob. 27HP Ch. 10.7 - Prob. 28HP Ch. 10.7 - Prob. 29HP Ch. 10.7 - Prob. 30HP Ch. 10.7 - Prob. 31HP Ch. 10.7 - Prob. 32STP Ch. 10.7 - Prob. 33STP Ch. 10.7 - Prob. 34STP Ch. 10.7 - Prob. 35STP Ch. 10.7 - Prob. 36SPR Ch. 10.7 - Prob. 37SPR Ch. 10.7 - Prob. 38SPR Ch. 10.7 - Prob. 39SPR Ch. 10.7 - Prob. 40SPR Ch. 10.7 - Prob. 41SPR Ch. 10.7 - Prob. 42SPR Ch. 10.7 - Prob. 43SPR Ch. 10.7 - Prob. 44SR Ch. 10.7 - Prob. 45SR Ch. 10.7 - Prob. 46SR Ch. 10.7 - Prob. 47SR Ch. 10.7 - Prob. 48SR Ch. 10.7 - Prob. 49SR Ch. 10.8 - Prob. 1ACYP Ch. 10.8 - Prob. 1BCYP Ch. 10.8 - Prob. 2ACYP Ch. 10.8 - Prob. 2BCYP Ch. 10.8 - Prob. 3ACYP Ch. 10.8 - Prob. 3BCYP Ch. 10.8 - Prob. 4CYP Ch. 10.8 - Prob. 1CYU Ch. 10.8 - Prob. 2CYU Ch. 10.8 - Prob. 3CYU Ch. 10.8 - Prob. 4CYU Ch. 10.8 - Prob. 5CYU Ch. 10.8 - Prob. 6CYU Ch. 10.8 - Prob. 7CYU Ch. 10.8 - Prob. 8CYU Ch. 10.8 - Prob. 9CYU Ch. 10.8 - Prob. 10CYU Ch. 10.8 - Prob. 11PPS Ch. 10.8 - Prob. 12PPS Ch. 10.8 - Prob. 13PPS Ch. 10.8 - Prob. 14PPS Ch. 10.8 - Prob. 15PPS Ch. 10.8 - Prob. 16PPS Ch. 10.8 - Prob. 17PPS Ch. 10.8 - Prob. 18PPS Ch. 10.8 - Prob. 19PPS Ch. 10.8 - Prob. 20PPS Ch. 10.8 - Prob. 21PPS Ch. 10.8 - Prob. 22PPS Ch. 10.8 - Prob. 23PPS Ch. 10.8 - Prob. 24PPS Ch. 10.8 - Prob. 25PPS Ch. 10.8 - Prob. 26PPS Ch. 10.8 - Prob. 27PPS Ch. 10.8 - Prob. 28PPS Ch. 10.8 - Prob. 29PPS Ch. 10.8 - Prob. 30PPS Ch. 10.8 - Prob. 31PPS Ch. 10.8 - Prob. 32PPS Ch. 10.8 - Prob. 33PPS Ch. 10.8 - Prob. 34PPS Ch. 10.8 - Prob. 35PPS Ch. 10.8 - Prob. 36HP Ch. 10.8 - Prob. 37HP Ch. 10.8 - Prob. 38HP Ch. 10.8 - Prob. 39HP Ch. 10.8 - Prob. 40HP Ch. 10.8 - Prob. 41STP Ch. 10.8 - Prob. 42STP Ch. 10.8 - Prob. 43STP Ch. 10.8 - Prob. 44STP Ch. 10.8 - Prob. 45SPR Ch. 10.8 - Prob. 46SPR Ch. 10.8 - Prob. 47SPR Ch. 10.8 - Prob. 48SPR Ch. 10.8 - Prob. 49SPR Ch. 10.8 - Prob. 50SPR Ch. 10.8 - Prob. 51SPR Ch. 10.8 - Prob. 52SR Ch. 10.8 - Prob. 53SR Ch. 10.8 - Prob. 54SR Ch. 10 - Prob. 1GRFC Ch. 10 - 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