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High School Math Geometry Geometry, Student Edition

To prove: The relation K P = K Q = K R .

To prove: The relation K P = K Q = K R .

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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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 5.1, Problem 38PPS

To determine

To prove: The relation KP=KQ=KR .

Expert Solution & Answer

Explanation of Solution

Given information:

The given triangle shown in figure (1).

Geometry, Student Edition, Chapter 5.1, Problem 38PPS

Figure (1)

Th given relations are.

AD¯,BE¯,CF¯KP¯⊥AB¯,KQ¯⊥BC¯,KR¯⊥AC¯

Proof:

Using the definition of incenter,

K is in center of ΔABC .

Using incenter theorem.

KP=KQ, KQ=KR, KP=KR

Using transitive property.

KP=KQ=KR

From the above, KP=KQ=KR .

Hence, proved.

Chapter 5.1, Problem 37PPS

Chapter 5.1, Problem 39PPS

Chapter 5 Solutions

Geometry, Student Edition

Ch. 5.1 - Prob. 1ACYP Ch. 5.1 - Prob. 1BCYP Ch. 5.1 - Prob. 1CCYP Ch. 5.1 - Prob. 2CYP Ch. 5.1 - Prob. 3ACYP Ch. 5.1 - Prob. 3BCYP Ch. 5.1 - Prob. 3CCYP Ch. 5.1 - Prob. 4ACYP Ch. 5.1 - Prob. 4BCYP Ch. 5.1 - Prob. 1CYU

Ch. 5.1 - Prob. 2CYU Ch. 5.1 - Prob. 3CYU Ch. 5.1 - Prob. 4CYU Ch. 5.1 - Prob. 5CYU Ch. 5.1 - Prob. 6CYU Ch. 5.1 - Prob. 7CYU Ch. 5.1 - Prob. 8CYU Ch. 5.1 - Prob. 9PPS Ch. 5.1 - Prob. 10PPS Ch. 5.1 - Prob. 11PPS Ch. 5.1 - Prob. 12PPS Ch. 5.1 - Prob. 13PPS Ch. 5.1 - Prob. 14PPS Ch. 5.1 - Prob. 15PPS Ch. 5.1 - Prob. 16PPS Ch. 5.1 - Prob. 17PPS Ch. 5.1 - Prob. 18PPS Ch. 5.1 - Prob. 19PPS Ch. 5.1 - Prob. 20PPS Ch. 5.1 - Prob. 21PPS Ch. 5.1 - Prob. 22PPS Ch. 5.1 - Prob. 23PPS Ch. 5.1 - Prob. 24PPS Ch. 5.1 - Prob. 25PPS Ch. 5.1 - Prob. 26PPS Ch. 5.1 - Prob. 27PPS Ch. 5.1 - Prob. 28PPS Ch. 5.1 - Prob. 29PPS Ch. 5.1 - Prob. 30PPS Ch. 5.1 - Prob. 31PPS Ch. 5.1 - Prob. 32PPS Ch. 5.1 - Prob. 33PPS Ch. 5.1 - Prob. 34PPS Ch. 5.1 - Prob. 35PPS Ch. 5.1 - Prob. 36PPS Ch. 5.1 - Prob. 37PPS Ch. 5.1 - Prob. 38PPS Ch. 5.1 - Prob. 39PPS Ch. 5.1 - Prob. 40PPS Ch. 5.1 - Prob. 41PPS Ch. 5.1 - Prob. 42PPS Ch. 5.1 - Prob. 43PPS Ch. 5.1 - Prob. 44PPS Ch. 5.1 - Prob. 45PPS Ch. 5.1 - Prob. 46PPS Ch. 5.1 - Prob. 47PPS Ch. 5.1 - Prob. 48HP Ch. 5.1 - Prob. 49HP Ch. 5.1 - Prob. 50HP Ch. 5.1 - Prob. 51HP Ch. 5.1 - Prob. 52HP Ch. 5.1 - Prob. 53HP Ch. 5.1 - Prob. 54HP Ch. 5.1 - Prob. 55STP Ch. 5.1 - Prob. 56STP Ch. 5.1 - Prob. 57STP Ch. 5.1 - Prob. 58STP Ch. 5.1 - Prob. 59SPR Ch. 5.1 - Prob. 60SPR Ch. 5.1 - Prob. 61SPR Ch. 5.1 - Prob. 62SPR Ch. 5.1 - Prob. 63SPR Ch. 5.1 - Prob. 64SPR Ch. 5.1 - Prob. 65SPR Ch. 5.1 - Prob. 66SPR Ch. 5.1 - Prob. 67SPR Ch. 5.1 - Prob. 68SR Ch. 5.1 - Prob. 69SR Ch. 5.2 - Prob. 1ACYP Ch. 5.2 - Prob. 1BCYP Ch. 5.2 - Prob. 2ACYP Ch. 5.2 - Prob. 2BCYP Ch. 5.2 - Prob. 3CYP Ch. 5.2 - Prob. 4CYP Ch. 5.2 - Prob. 1CYU Ch. 5.2 - Prob. 2CYU Ch. 5.2 - Prob. 3CYU Ch. 5.2 - Prob. 4CYU Ch. 5.2 - Prob. 5PPS Ch. 5.2 - Prob. 6PPS Ch. 5.2 - Prob. 7PPS Ch. 5.2 - Prob. 8PPS Ch. 5.2 - Prob. 9PPS Ch. 5.2 - Prob. 10PPS Ch. 5.2 - Prob. 11PPS Ch. 5.2 - Prob. 12PPS Ch. 5.2 - Prob. 13PPS Ch. 5.2 - Prob. 14PPS Ch. 5.2 - Prob. 15PPS Ch. 5.2 - Prob. 16PPS Ch. 5.2 - Prob. 17PPS Ch. 5.2 - Prob. 18PPS Ch. 5.2 - Prob. 19PPS Ch. 5.2 - 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Prob. 6CYU Ch. 5.3 - Prob. 7CYU Ch. 5.3 - Prob. 8PPS Ch. 5.3 - Prob. 9PPS Ch. 5.3 - Prob. 10PPS Ch. 5.3 - Prob. 11PPS Ch. 5.3 - Prob. 12PPS Ch. 5.3 - Prob. 13PPS Ch. 5.3 - Prob. 14PPS Ch. 5.3 - Prob. 15PPS Ch. 5.3 - Prob. 16PPS Ch. 5.3 - Prob. 17PPS Ch. 5.3 - Prob. 18PPS Ch. 5.3 - Prob. 19PPS Ch. 5.3 - Prob. 20PPS Ch. 5.3 - Prob. 21PPS Ch. 5.3 - Prob. 22PPS Ch. 5.3 - Prob. 23PPS Ch. 5.3 - Prob. 24PPS Ch. 5.3 - Prob. 25PPS Ch. 5.3 - Prob. 26PPS Ch. 5.3 - Prob. 27PPS Ch. 5.3 - Prob. 28PPS Ch. 5.3 - Prob. 29PPS Ch. 5.3 - Prob. 30PPS Ch. 5.3 - Prob. 31PPS Ch. 5.3 - Prob. 32PPS Ch. 5.3 - Prob. 33PPS Ch. 5.3 - Prob. 34PPS Ch. 5.3 - Prob. 35PPS Ch. 5.3 - Prob. 36PPS Ch. 5.3 - Prob. 37PPS Ch. 5.3 - Prob. 38PPS Ch. 5.3 - Prob. 39PPS Ch. 5.3 - Prob. 40PPS Ch. 5.3 - Prob. 41PPS Ch. 5.3 - Prob. 42PPS Ch. 5.3 - Prob. 43HP Ch. 5.3 - Prob. 44HP Ch. 5.3 - Prob. 45HP Ch. 5.3 - Prob. 46HP Ch. 5.3 - Prob. 47HP Ch. 5.3 - Prob. 48HP Ch. 5.3 - Prob. 49STP Ch. 5.3 - Prob. 50STP Ch. 5.3 - Prob. 51STP Ch. 5.3 - 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Prob. 30PPS Ch. 5.4 - Prob. 31PPS Ch. 5.4 - Prob. 32PPS Ch. 5.4 - Prob. 33PPS Ch. 5.4 - Prob. 34PPS Ch. 5.4 - Prob. 35PPS Ch. 5.4 - Prob. 36PPS Ch. 5.4 - Prob. 37PPS Ch. 5.4 - Prob. 38PPS Ch. 5.4 - Prob. 39PPS Ch. 5.4 - Prob. 40HP Ch. 5.4 - Prob. 41HP Ch. 5.4 - Prob. 42HP Ch. 5.4 - Prob. 43HP Ch. 5.4 - Prob. 44HP Ch. 5.4 - Prob. 45STP Ch. 5.4 - Prob. 46STP Ch. 5.4 - Prob. 47STP Ch. 5.4 - Prob. 48STP Ch. 5.4 - Prob. 49SPR Ch. 5.4 - Prob. 50SPR Ch. 5.4 - Prob. 51SPR Ch. 5.4 - Prob. 52SPR Ch. 5.4 - Prob. 53SPR Ch. 5.4 - Prob. 54SPR Ch. 5.4 - Prob. 55SPR Ch. 5.4 - Prob. 56SPR Ch. 5.4 - Prob. 57SR Ch. 5.4 - Prob. 58SR Ch. 5.4 - Prob. 59SR Ch. 5.5 - Prob. 1ACYP Ch. 5.5 - Prob. 1BCYP Ch. 5.5 - Prob. 2CYP Ch. 5.5 - Prob. 3CYP Ch. 5.5 - Prob. 1CYU Ch. 5.5 - Prob. 2CYU Ch. 5.5 - Prob. 3CYU Ch. 5.5 - Prob. 4CYU Ch. 5.5 - Prob. 5CYU Ch. 5.5 - Prob. 6PPS Ch. 5.5 - Prob. 7PPS Ch. 5.5 - Prob. 8PPS Ch. 5.5 - Prob. 9PPS Ch. 5.5 - Prob. 10PPS Ch. 5.5 - Prob. 11PPS Ch. 5.5 - Prob. 12PPS Ch. 5.5 - Prob. 13PPS Ch. 5.5 - Prob. 14PPS Ch. 5.5 - Prob. 15PPS Ch. 5.5 - Prob. 16PPS Ch. 5.5 - Prob. 17PPS Ch. 5.5 - Prob. 18PPS Ch. 5.5 - Prob. 19PPS Ch. 5.5 - Prob. 20PPS Ch. 5.5 - Prob. 21PPS Ch. 5.5 - Prob. 22PPS Ch. 5.5 - Prob. 23PPS Ch. 5.5 - Prob. 24PPS Ch. 5.5 - Prob. 25PPS Ch. 5.5 - Prob. 26PPS Ch. 5.5 - Prob. 27PPS Ch. 5.5 - Prob. 28PPS Ch. 5.5 - Prob. 29PPS Ch. 5.5 - Prob. 30PPS Ch. 5.5 - Prob. 31PPS Ch. 5.5 - Prob. 32PPS Ch. 5.5 - Prob. 33PPS Ch. 5.5 - Prob. 34PPS Ch. 5.5 - Prob. 35PPS Ch. 5.5 - Prob. 36PPS Ch. 5.5 - Prob. 37PPS Ch. 5.5 - Prob. 38PPS Ch. 5.5 - Prob. 39PPS Ch. 5.5 - Prob. 40PPS Ch. 5.5 - Prob. 41PPS Ch. 5.5 - Prob. 42PPS Ch. 5.5 - Prob. 43HP Ch. 5.5 - Prob. 44HP Ch. 5.5 - Prob. 45HP Ch. 5.5 - Prob. 46HP Ch. 5.5 - Prob. 47HP Ch. 5.5 - Prob. 48HP Ch. 5.5 - Prob. 49STP Ch. 5.5 - Prob. 50STP Ch. 5.5 - Prob. 51STP Ch. 5.5 - Prob. 52STP Ch. 5.5 - Prob. 53SPR Ch. 5.5 - Prob. 54SPR Ch. 5.5 - Prob. 55SPR Ch. 5.5 - Prob. 56SPR Ch. 5.5 - Prob. 57SPR Ch. 5.5 - Prob. 58SPR Ch. 5.5 - Prob. 59SPR Ch. 5.5 - Prob. 60SPR Ch. 5.5 - Prob. 61SR Ch. 5.5 - Prob. 62SR Ch. 5.5 - Prob. 63SR Ch. 5.6 - Prob. 1ACYP Ch. 5.6 - Prob. 1BCYP Ch. 5.6 - Prob. 2ACYP Ch. 5.6 - Prob. 2BCYP Ch. 5.6 - Prob. 3CYP Ch. 5.6 - Prob. 4CYP Ch. 5.6 - Prob. 5CYP Ch. 5.6 - Prob. 1CYU Ch. 5.6 - Prob. 2CYU Ch. 5.6 - Prob. 3CYU Ch. 5.6 - Prob. 4CYU Ch. 5.6 - Prob. 5CYU Ch. 5.6 - Prob. 6CYU Ch. 5.6 - Prob. 7CYU Ch. 5.6 - Prob. 8CYU Ch. 5.6 - Prob. 9CYU Ch. 5.6 - Prob. 10PPS Ch. 5.6 - Prob. 11PPS Ch. 5.6 - Prob. 12PPS Ch. 5.6 - Prob. 13PPS Ch. 5.6 - Prob. 14PPS Ch. 5.6 - Prob. 15PPS Ch. 5.6 - Prob. 16PPS Ch. 5.6 - Prob. 17PPS Ch. 5.6 - Prob. 18PPS Ch. 5.6 - Prob. 19PPS Ch. 5.6 - Prob. 20PPS Ch. 5.6 - Prob. 21PPS Ch. 5.6 - Prob. 22PPS Ch. 5.6 - Prob. 23PPS Ch. 5.6 - Prob. 24PPS Ch. 5.6 - Prob. 25PPS Ch. 5.6 - Prob. 26PPS Ch. 5.6 - Prob. 27PPS Ch. 5.6 - Prob. 28PPS Ch. 5.6 - Prob. 29PPS Ch. 5.6 - Prob. 30PPS Ch. 5.6 - Prob. 31PPS Ch. 5.6 - Prob. 32PPS Ch. 5.6 - Prob. 33PPS Ch. 5.6 - Prob. 34PPS Ch. 5.6 - Prob. 35PPS Ch. 5.6 - Prob. 36PPS Ch. 5.6 - Prob. 37PPS Ch. 5.6 - Prob. 38HP Ch. 5.6 - Prob. 39HP Ch. 5.6 - Prob. 40HP Ch. 5.6 - Prob. 41HP Ch. 5.6 - Prob. 42HP Ch. 5.6 - Prob. 43STP Ch. 5.6 - Prob. 44STP Ch. 5.6 - Prob. 45STP Ch. 5.6 - Prob. 46STP Ch. 5.6 - Prob. 47SPR Ch. 5.6 - Prob. 48SPR Ch. 5.6 - Prob. 49SPR Ch. 5.6 - Prob. 50SPR Ch. 5.6 - Prob. 51SPR Ch. 5.6 - Prob. 52SPR Ch. 5.6 - Prob. 53SPR Ch. 5.6 - Prob. 54SPR Ch. 5.6 - Prob. 55SPR Ch. 5.6 - Prob. 56SR Ch. 5.6 - Prob. 57SR Ch. 5.6 - Prob. 58SR Ch. 5 - Prob. 1GRFC Ch. 5 - Prob. 2GRFC Ch. 5 - Prob. 3GRFC Ch. 5 - Prob. 4GRFC Ch. 5 - Prob. 5GRFC Ch. 5 - Prob. 6GRFC Ch. 5 - Prob. 7GRFC Ch. 5 - Prob. 8GRFC Ch. 5 - Prob. 9GRFC Ch. 5 - Prob. 10GRFC Ch. 5 - Prob. 11GRFC Ch. 5 - Prob. 12GRFC Ch. 5 - Prob. 1MCQ Ch. 5 - Prob. 2MCQ Ch. 5 - Prob. 3MCQ Ch. 5 - Prob. 4MCQ Ch. 5 - Prob. 5MCQ Ch. 5 - Prob. 6MCQ Ch. 5 - Prob. 7MCQ Ch. 5 - Prob. 8MCQ Ch. 5 - Prob. 9MCQ Ch. 5 - Prob. 10MCQ Ch. 5 - Prob. 11MCQ Ch. 5 - Prob. 12MCQ Ch. 5 - Prob. 13MCQ Ch. 5 - Prob. 14MCQ Ch. 5 - Prob. 15MCQ Ch. 5 - Prob. 16MCQ Ch. 5 - Prob. 17MCQ Ch. 5 - Prob. 18MCQ Ch. 5 - Prob. 19MCQ Ch. 5 - Prob. 1SGR Ch. 5 - Prob. 2SGR Ch. 5 - Prob. 3SGR Ch. 5 - Prob. 4SGR Ch. 5 - Prob. 5SGR Ch. 5 - Prob. 6SGR Ch. 5 - Prob. 7SGR Ch. 5 - Prob. 8SGR Ch. 5 - Prob. 9SGR Ch. 5 - Prob. 10SGR Ch. 5 - Prob. 11SGR Ch. 5 - Prob. 12SGR Ch. 5 - Prob. 13SGR Ch. 5 - Prob. 14SGR Ch. 5 - Prob. 15SGR Ch. 5 - Prob. 16SGR Ch. 5 - Prob. 17SGR Ch. 5 - Prob. 18SGR Ch. 5 - Prob. 19SGR Ch. 5 - Prob. 20SGR Ch. 5 - Prob. 21SGR Ch. 5 - Prob. 22SGR Ch. 5 - Prob. 23SGR Ch. 5 - Prob. 24SGR Ch. 5 - Prob. 25SGR Ch. 5 - Prob. 26SGR Ch. 5 - Prob. 27SGR Ch. 5 - Prob. 28SGR Ch. 5 - Prob. 29SGR Ch. 5 - Prob. 30SGR Ch. 5 - Prob. 31SGR Ch. 5 - Prob. 32SGR Ch. 5 - Prob. 33SGR Ch. 5 - Prob. 1PT Ch. 5 - Prob. 2PT Ch. 5 - Prob. 3PT Ch. 5 - Prob. 4PT Ch. 5 - Prob. 5PT Ch. 5 - Prob. 6PT Ch. 5 - Prob. 7PT Ch. 5 - Prob. 8PT Ch. 5 - Prob. 9PT Ch. 5 - Prob. 10PT Ch. 5 - Prob. 11PT Ch. 5 - Prob. 12PT Ch. 5 - Prob. 13PT Ch. 5 - Prob. 14PT Ch. 5 - Prob. 15PT Ch. 5 - 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