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High School Math Geometry Geometry, Student Edition

Whether the two given triangles are always, sometimes or never similar. Then, explain the reasoning.

Whether the two given triangles are always, sometimes or never similar. Then, explain the reasoning.

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 7.2, Problem 45PPS

To determine

To find: Whether the two given triangles are always, sometimes or never similar. Then, explain the reasoning.

Expert Solution & Answer

Answer to Problem 45PPS

The equilateral triangles are always similar by the theorem of similar polygons.

Explanation of Solution

Given:

The give triangles are tow equilateral triangle.

Calculation:

Consider that the two polygons are similar when the corresponding angles are similar and the corresponding side length are proportional.

Consider that a triangle is scalene if two sides are congruent and a triangle is isosceles if at least two sides are congruent.

Consider that a equilateral triangle has all the sides and the angle congruent. Thus, two equilateral triangles have same angles and sides in proportion.

Thus, two equilateral triangles are always similar by the theorem of similar polygons.

Chapter 7.2, Problem 44PPS

Chapter 7.2, Problem 46PPS

Chapter 7 Solutions

Geometry, Student Edition

Ch. 7.1 - Prob. 1ACYP Ch. 7.1 - Prob. 2CYP Ch. 7.1 - Prob. 3ACYP Ch. 7.1 - Prob. 3BCYP Ch. 7.1 - Prob. 3CCYP Ch. 7.1 - Prob. 4CYP Ch. 7.1 - Prob. 1CYU Ch. 7.1 - Prob. 2CYU Ch. 7.1 - Prob. 3CYU Ch. 7.1 - Prob. 4CYU

Ch. 7.1 - Prob. 5CYU Ch. 7.1 - Prob. 6CYU Ch. 7.1 - Prob. 7CYU Ch. 7.1 - Prob. 8CYU Ch. 7.1 - Prob. 9CYU Ch. 7.1 - Prob. 10PPS Ch. 7.1 - Prob. 11PPS Ch. 7.1 - Prob. 12PPS Ch. 7.1 - Prob. 13PPS Ch. 7.1 - Prob. 14PPS Ch. 7.1 - Prob. 15PPS Ch. 7.1 - Prob. 16PPS Ch. 7.1 - Prob. 17PPS Ch. 7.1 - Prob. 18PPS Ch. 7.1 - Prob. 19PPS Ch. 7.1 - Prob. 20PPS Ch. 7.1 - Prob. 21PPS Ch. 7.1 - Prob. 22PPS Ch. 7.1 - Prob. 23PPS Ch. 7.1 - Prob. 24PPS Ch. 7.1 - Prob. 25PPS Ch. 7.1 - Prob. 26PPS Ch. 7.1 - Prob. 27PPS Ch. 7.1 - Prob. 28PPS Ch. 7.1 - Prob. 29PPS Ch. 7.1 - Prob. 30PPS Ch. 7.1 - Prob. 31PPS Ch. 7.1 - Prob. 32PPS Ch. 7.1 - Prob. 33PPS Ch. 7.1 - Prob. 34PPS Ch. 7.1 - Prob. 35PPS Ch. 7.1 - Prob. 36PPS Ch. 7.1 - Prob. 37PPS Ch. 7.1 - Prob. 38PPS Ch. 7.1 - Prob. 39PPS Ch. 7.1 - Prob. 40PPS Ch. 7.1 - Prob. 41PPS Ch. 7.1 - Prob. 42PPS Ch. 7.1 - Prob. 43PPS Ch. 7.1 - Prob. 44HP Ch. 7.1 - Prob. 45HP Ch. 7.1 - Prob. 46HP Ch. 7.1 - Prob. 47HP Ch. 7.1 - Prob. 48HP Ch. 7.1 - Prob. 49HP Ch. 7.1 - Prob. 50STP Ch. 7.1 - Prob. 51STP Ch. 7.1 - Prob. 52STP Ch. 7.1 - Prob. 53STP Ch. 7.1 - Prob. 54SPR Ch. 7.1 - Prob. 55SPR Ch. 7.1 - Prob. 56SPR Ch. 7.1 - Prob. 57SPR Ch. 7.1 - Prob. 58SPR Ch. 7.1 - Prob. 59SPR Ch. 7.1 - Prob. 60SPR Ch. 7.1 - Prob. 61SPR Ch. 7.1 - Prob. 62SPR Ch. 7.1 - Prob. 63SPR Ch. 7.1 - Prob. 64SPR Ch. 7.1 - Prob. 65SR Ch. 7.2 - Prob. 1CYP Ch. 7.2 - Prob. 2CYP Ch. 7.2 - Prob. 3ACYP Ch. 7.2 - Prob. 3BCYP Ch. 7.2 - Prob. 4CYP Ch. 7.2 - Prob. 1CYU Ch. 7.2 - Prob. 2CYU Ch. 7.2 - Prob. 3CYU Ch. 7.2 - Prob. 4CYU Ch. 7.2 - Prob. 5CYU Ch. 7.2 - Prob. 6CYU Ch. 7.2 - Prob. 7CYU Ch. 7.2 - Prob. 8PPS Ch. 7.2 - Prob. 9PPS Ch. 7.2 - Prob. 10PPS Ch. 7.2 - Prob. 11PPS Ch. 7.2 - Prob. 12PPS Ch. 7.2 - Prob. 13PPS Ch. 7.2 - Prob. 14PPS Ch. 7.2 - Prob. 15PPS Ch. 7.2 - Prob. 16PPS Ch. 7.2 - Prob. 17PPS Ch. 7.2 - Prob. 18PPS Ch. 7.2 - Prob. 19PPS Ch. 7.2 - Prob. 20PPS Ch. 7.2 - Prob. 21PPS Ch. 7.2 - Prob. 22PPS Ch. 7.2 - Prob. 23PPS Ch. 7.2 - Prob. 24PPS Ch. 7.2 - Prob. 25PPS Ch. 7.2 - Prob. 26PPS Ch. 7.2 - Prob. 27PPS Ch. 7.2 - Prob. 28PPS Ch. 7.2 - Prob. 29PPS Ch. 7.2 - Prob. 30PPS Ch. 7.2 - Prob. 31PPS Ch. 7.2 - Prob. 32PPS Ch. 7.2 - Prob. 33PPS Ch. 7.2 - Prob. 34PPS Ch. 7.2 - Prob. 35PPS Ch. 7.2 - Prob. 36PPS Ch. 7.2 - Prob. 37PPS Ch. 7.2 - Prob. 38PPS Ch. 7.2 - Prob. 39PPS Ch. 7.2 - Prob. 40PPS Ch. 7.2 - Prob. 41PPS Ch. 7.2 - Prob. 42PPS Ch. 7.2 - Prob. 43PPS Ch. 7.2 - Prob. 44PPS Ch. 7.2 - Prob. 45PPS Ch. 7.2 - Prob. 46PPS Ch. 7.2 - Prob. 47PPS Ch. 7.2 - Prob. 48PPS Ch. 7.2 - Prob. 49PPS Ch. 7.2 - Prob. 50PPS Ch. 7.2 - Prob. 51HP Ch. 7.2 - Prob. 52HP Ch. 7.2 - Prob. 53HP Ch. 7.2 - Prob. 54HP Ch. 7.2 - Prob. 55HP Ch. 7.2 - Prob. 56STP Ch. 7.2 - Prob. 57STP Ch. 7.2 - Prob. 58STP Ch. 7.2 - Prob. 59STP Ch. 7.2 - Prob. 60SPR Ch. 7.2 - Prob. 61SPR Ch. 7.2 - Prob. 62SPR Ch. 7.2 - Prob. 63SPR Ch. 7.2 - Prob. 64SPR Ch. 7.2 - Prob. 65SPR Ch. 7.2 - Prob. 66SPR Ch. 7.2 - Prob. 67SPR Ch. 7.2 - Prob. 68SPR Ch. 7.2 - Prob. 69SPR Ch. 7.2 - Prob. 70SR Ch. 7.2 - Prob. 71SR Ch. 7.2 - Prob. 72SR Ch. 7.3 - Prob. 1ACYP Ch. 7.3 - Prob. 1BCYP Ch. 7.3 - Prob. 2ACYP Ch. 7.3 - Prob. 2BCYP Ch. 7.3 - Prob. 3CYP Ch. 7.3 - Prob. 4ACYP Ch. 7.3 - Prob. 4BCYP Ch. 7.3 - Prob. 5CYP Ch. 7.3 - Prob. 1CYU Ch. 7.3 - Prob. 2CYU Ch. 7.3 - Prob. 3CYU Ch. 7.3 - Prob. 4CYU Ch. 7.3 - Prob. 5CYU Ch. 7.3 - Prob. 6CYU Ch. 7.3 - Prob. 7CYU Ch. 7.3 - Prob. 8CYU Ch. 7.3 - Prob. 9PPS Ch. 7.3 - Prob. 10PPS Ch. 7.3 - Prob. 11PPS Ch. 7.3 - Prob. 12PPS Ch. 7.3 - Prob. 13PPS Ch. 7.3 - Prob. 14PPS Ch. 7.3 - Prob. 15PPS Ch. 7.3 - Prob. 16PPS Ch. 7.3 - Prob. 17PPS Ch. 7.3 - Prob. 18PPS Ch. 7.3 - Prob. 19PPS Ch. 7.3 - Prob. 20PPS Ch. 7.3 - Prob. 21PPS Ch. 7.3 - Prob. 22PPS Ch. 7.3 - Prob. 23PPS Ch. 7.3 - Prob. 24PPS Ch. 7.3 - Prob. 25PPS Ch. 7.3 - Prob. 26PPS Ch. 7.3 - Prob. 27PPS Ch. 7.3 - Prob. 28PPS Ch. 7.3 - Prob. 29PPS Ch. 7.3 - Prob. 30PPS Ch. 7.3 - Prob. 31PPS Ch. 7.3 - Prob. 32PPS Ch. 7.3 - Prob. 33PPS Ch. 7.3 - Prob. 34PPS Ch. 7.3 - Prob. 35PPS Ch. 7.3 - Prob. 36PPS Ch. 7.3 - Prob. 37HP Ch. 7.3 - Prob. 38HP Ch. 7.3 - Prob. 39HP Ch. 7.3 - Prob. 40HP Ch. 7.3 - Prob. 41HP Ch. 7.3 - Prob. 42STP Ch. 7.3 - Prob. 43STP Ch. 7.3 - Prob. 44STP Ch. 7.3 - Prob. 45STP Ch. 7.3 - Prob. 46SPR Ch. 7.3 - Prob. 47SPR Ch. 7.3 - Prob. 48SPR Ch. 7.3 - Prob. 49SPR Ch. 7.3 - Prob. 50SPR Ch. 7.3 - Prob. 51SPR Ch. 7.3 - Prob. 52SPR Ch. 7.3 - Prob. 53SPR Ch. 7.3 - Prob. 54SPR Ch. 7.3 - Prob. 55SPR Ch. 7.3 - Prob. 56SPR Ch. 7.3 - Prob. 57SR Ch. 7.4 - Prob. 1CYP Ch. 7.4 - Prob. 2CYP Ch. 7.4 - Prob. 3ACYP Ch. 7.4 - Prob. 3BCYP Ch. 7.4 - Prob. 3CCYP Ch. 7.4 - Prob. 4CYP Ch. 7.4 - Prob. 5ACYP Ch. 7.4 - Prob. 5BCYP Ch. 7.4 - Prob. 1CYU Ch. 7.4 - Prob. 2CYU Ch. 7.4 - Prob. 3CYU Ch. 7.4 - Prob. 4CYU Ch. 7.4 - Prob. 5CYU Ch. 7.4 - Prob. 6CYU Ch. 7.4 - Prob. 7CYU Ch. 7.4 - Prob. 8CYU Ch. 7.4 - Prob. 9CYU Ch. 7.4 - Prob. 10PPS Ch. 7.4 - Prob. 11PPS Ch. 7.4 - Prob. 12PPS Ch. 7.4 - Prob. 13PPS Ch. 7.4 - Prob. 14PPS Ch. 7.4 - Prob. 15PPS Ch. 7.4 - Prob. 16PPS Ch. 7.4 - Prob. 17PPS Ch. 7.4 - Prob. 18PPS Ch. 7.4 - Prob. 19PPS Ch. 7.4 - Prob. 20PPS Ch. 7.4 - Prob. 21PPS Ch. 7.4 - Prob. 22PPS Ch. 7.4 - Prob. 23PPS Ch. 7.4 - Prob. 24PPS Ch. 7.4 - Prob. 25PPS Ch. 7.4 - Prob. 26PPS Ch. 7.4 - Prob. 27PPS Ch. 7.4 - Prob. 28PPS Ch. 7.4 - Prob. 29PPS Ch. 7.4 - Prob. 30PPS Ch. 7.4 - Prob. 31PPS Ch. 7.4 - Prob. 32PPS Ch. 7.4 - Prob. 33PPS Ch. 7.4 - Prob. 34PPS Ch. 7.4 - Prob. 35PPS Ch. 7.4 - Prob. 36PPS Ch. 7.4 - Prob. 37PPS Ch. 7.4 - Prob. 38PPS Ch. 7.4 - Prob. 39PPS Ch. 7.4 - Prob. 40PPS Ch. 7.4 - Prob. 41PPS Ch. 7.4 - Prob. 42PPS Ch. 7.4 - Prob. 43PPS Ch. 7.4 - Prob. 44PPS Ch. 7.4 - Prob. 45PPS Ch. 7.4 - Prob. 46PPS Ch. 7.4 - Prob. 47PPS Ch. 7.4 - Prob. 48HP Ch. 7.4 - Prob. 49HP Ch. 7.4 - Prob. 50HP Ch. 7.4 - Prob. 51HP Ch. 7.4 - Prob. 52HP Ch. 7.4 - Prob. 53STP Ch. 7.4 - Prob. 54STP Ch. 7.4 - Prob. 55STP Ch. 7.4 - Prob. 56STP Ch. 7.4 - Prob. 57SPR Ch. 7.4 - Prob. 58SPR Ch. 7.4 - Prob. 59SPR Ch. 7.4 - Prob. 60SPR Ch. 7.4 - Prob. 61SPR Ch. 7.4 - Prob. 62SPR Ch. 7.4 - Prob. 63SPR Ch. 7.4 - Prob. 64SPR Ch. 7.4 - Prob. 65SPR Ch. 7.4 - Prob. 66SPR Ch. 7.4 - Prob. 67SR Ch. 7.4 - Prob. 68SR Ch. 7.4 - Prob. 69SR Ch. 7.4 - Prob. 70SR Ch. 7.4 - Prob. 71SR Ch. 7.5 - Prob. 1ACYP Ch. 7.5 - Prob. 1BCYP Ch. 7.5 - Prob. 2CYP Ch. 7.5 - Prob. 3ACYP Ch. 7.5 - Prob. 3BCYP Ch. 7.5 - Prob. 1CYU Ch. 7.5 - Prob. 2CYU Ch. 7.5 - Prob. 3CYU Ch. 7.5 - Prob. 4CYU Ch. 7.5 - Prob. 5CYU Ch. 7.5 - Prob. 6PPS Ch. 7.5 - Prob. 7PPS Ch. 7.5 - Prob. 8PPS Ch. 7.5 - Prob. 9PPS Ch. 7.5 - Prob. 10PPS Ch. 7.5 - Prob. 11PPS Ch. 7.5 - Prob. 12PPS Ch. 7.5 - Prob. 13PPS Ch. 7.5 - Prob. 14PPS Ch. 7.5 - Prob. 15PPS Ch. 7.5 - Prob. 16PPS Ch. 7.5 - Prob. 17PPS Ch. 7.5 - Prob. 18PPS Ch. 7.5 - Prob. 19PPS Ch. 7.5 - Prob. 20PPS Ch. 7.5 - Prob. 21PPS Ch. 7.5 - Prob. 22PPS Ch. 7.5 - Prob. 23PPS Ch. 7.5 - Prob. 24PPS Ch. 7.5 - Prob. 25PPS Ch. 7.5 - Prob. 26PPS Ch. 7.5 - Prob. 27PPS Ch. 7.5 - Prob. 28PPS Ch. 7.5 - Prob. 29PPS Ch. 7.5 - Prob. 30PPS Ch. 7.5 - Prob. 31HP Ch. 7.5 - Prob. 32HP Ch. 7.5 - Prob. 33HP Ch. 7.5 - Prob. 34HP Ch. 7.5 - Prob. 35HP Ch. 7.5 - Prob. 36STP Ch. 7.5 - Prob. 37STP Ch. 7.5 - Prob. 38STP Ch. 7.5 - Prob. 39STP Ch. 7.5 - Prob. 40SPR Ch. 7.5 - Prob. 41SPR Ch. 7.5 - Prob. 42SPR Ch. 7.5 - Prob. 43SPR Ch. 7.5 - Prob. 44SPR Ch. 7.5 - Prob. 45SPR Ch. 7.5 - Prob. 46SR Ch. 7.5 - Prob. 47SR Ch. 7.5 - Prob. 48SR Ch. 7.5 - Prob. 49SR Ch. 7.5 - Prob. 50SR Ch. 7.5 - Prob. 51SR Ch. 7.6 - Prob. 1ACYP Ch. 7.6 - Prob. 1BCYP Ch. 7.6 - Prob. 2CYP Ch. 7.6 - Prob. 3ACYP Ch. 7.6 - Prob. 3BCYP Ch. 7.6 - Prob. 1CYU Ch. 7.6 - Prob. 2CYU Ch. 7.6 - Prob. 3CYU Ch. 7.6 - Prob. 4CYU Ch. 7.6 - Prob. 5CYU Ch. 7.6 - Prob. 6PPS Ch. 7.6 - Prob. 7PPS Ch. 7.6 - Prob. 8PPS Ch. 7.6 - Prob. 9PPS Ch. 7.6 - Prob. 10PPS Ch. 7.6 - Prob. 11PPS Ch. 7.6 - Prob. 12PPS Ch. 7.6 - Prob. 13PPS Ch. 7.6 - Prob. 14PPS Ch. 7.6 - Prob. 15PPS Ch. 7.6 - Prob. 16PPS Ch. 7.6 - Prob. 17PPS Ch. 7.6 - Prob. 18PPS Ch. 7.6 - Prob. 19PPS Ch. 7.6 - Prob. 20PPS Ch. 7.6 - Prob. 21PPS Ch. 7.6 - Prob. 22HP Ch. 7.6 - Prob. 23HP Ch. 7.6 - Prob. 24HP Ch. 7.6 - Prob. 25HP Ch. 7.6 - Prob. 26HP Ch. 7.6 - Prob. 27HP Ch. 7.6 - Prob. 28STP Ch. 7.6 - Prob. 29STP Ch. 7.6 - Prob. 30STP Ch. 7.6 - Prob. 31STP Ch. 7.6 - Prob. 32SPR Ch. 7.6 - Prob. 33SPR Ch. 7.6 - Prob. 34SPR Ch. 7.6 - Prob. 35SPR Ch. 7.6 - Prob. 36SPR Ch. 7.6 - Prob. 37SPR Ch. 7.6 - Prob. 38SPR Ch. 7.6 - Prob. 39SPR Ch. 7.6 - Prob. 40SR Ch. 7.6 - Prob. 41SR Ch. 7.6 - Prob. 42SR Ch. 7.6 - Prob. 43SR Ch. 7.6 - Prob. 44SR Ch. 7.6 - Prob. 45SR Ch. 7.7 - Prob. 1CYP Ch. 7.7 - Prob. 2CYP Ch. 7.7 - Prob. 3CYP Ch. 7.7 - Prob. 1CYU Ch. 7.7 - Prob. 2CYU Ch. 7.7 - Prob. 3CYU Ch. 7.7 - Prob. 4CYU Ch. 7.7 - Prob. 5PPS Ch. 7.7 - Prob. 6PPS Ch. 7.7 - Prob. 7PPS Ch. 7.7 - Prob. 8PPS Ch. 7.7 - Prob. 9PPS Ch. 7.7 - Prob. 10PPS Ch. 7.7 - Prob. 11PPS Ch. 7.7 - Prob. 12PPS Ch. 7.7 - Prob. 13PPS Ch. 7.7 - Prob. 14PPS Ch. 7.7 - Prob. 15PPS Ch. 7.7 - Prob. 16PPS Ch. 7.7 - Prob. 17PPS Ch. 7.7 - Prob. 18PPS Ch. 7.7 - Prob. 19PPS Ch. 7.7 - Prob. 20PPS Ch. 7.7 - Prob. 21HP Ch. 7.7 - Prob. 22HP Ch. 7.7 - Prob. 23HP Ch. 7.7 - Prob. 24HP Ch. 7.7 - Prob. 25HP Ch. 7.7 - Prob. 26STP Ch. 7.7 - Prob. 27STP Ch. 7.7 - Prob. 28STP Ch. 7.7 - Prob. 29STP Ch. 7.7 - Prob. 30SPR Ch. 7.7 - Prob. 31SPR Ch. 7.7 - Prob. 32SPR Ch. 7.7 - Prob. 33SPR Ch. 7.7 - Prob. 34SPR Ch. 7.7 - Prob. 35SPR Ch. 7.7 - Prob. 36SPR Ch. 7.7 - Prob. 37SPR Ch. 7.7 - Prob. 38SPR Ch. 7.7 - Prob. 39SPR Ch. 7.7 - Prob. 40SPR Ch. 7.7 - Prob. 41SPR Ch. 7.7 - Prob. 42SPR Ch. 7.7 - Prob. 43SPR Ch. 7.7 - Prob. 44SPR Ch. 7.7 - Prob. 45SR Ch. 7.7 - Prob. 46SR Ch. 7.7 - Prob. 47SR Ch. 7.7 - Prob. 48SR Ch. 7.7 - Prob. 49SR Ch. 7 - Prob. 1GRFC Ch. 7 - Prob. 2GRFC Ch. 7 - Prob. 3GRFC Ch. 7 - Prob. 4GRFC Ch. 7 - Prob. 5GRFC Ch. 7 - Prob. 6GRFC Ch. 7 - Prob. 7GRFC Ch. 7 - Prob. 8GRFC Ch. 7 - Prob. 1MCQ Ch. 7 - Prob. 2MCQ Ch. 7 - Prob. 3MCQ Ch. 7 - Prob. 4MCQ Ch. 7 - Prob. 5MCQ Ch. 7 - Prob. 6MCQ Ch. 7 - Prob. 7MCQ Ch. 7 - Prob. 8MCQ Ch. 7 - Prob. 9MCQ Ch. 7 - Prob. 10MCQ Ch. 7 - Prob. 11MCQ Ch. 7 - Prob. 12MCQ Ch. 7 - Prob. 13MCQ Ch. 7 - Prob. 14MCQ Ch. 7 - Prob. 15MCQ Ch. 7 - Prob. 1SGR Ch. 7 - Prob. 2SGR Ch. 7 - Prob. 3SGR Ch. 7 - Prob. 4SGR Ch. 7 - Prob. 5SGR Ch. 7 - Prob. 6SGR Ch. 7 - Prob. 7SGR Ch. 7 - Prob. 8SGR Ch. 7 - Prob. 9SGR Ch. 7 - Prob. 10SGR Ch. 7 - Prob. 11SGR Ch. 7 - Prob. 12SGR Ch. 7 - Prob. 13SGR Ch. 7 - Prob. 14SGR Ch. 7 - Prob. 15SGR Ch. 7 - Prob. 16SGR Ch. 7 - Prob. 17SGR Ch. 7 - Prob. 18SGR Ch. 7 - Prob. 19SGR Ch. 7 - Prob. 20SGR Ch. 7 - Prob. 21SGR Ch. 7 - Prob. 22SGR Ch. 7 - Prob. 23SGR Ch. 7 - Prob. 24SGR Ch. 7 - Prob. 25SGR Ch. 7 - Prob. 26SGR Ch. 7 - Prob. 27SGR Ch. 7 - Prob. 28SGR Ch. 7 - Prob. 29SGR Ch. 7 - Prob. 30SGR Ch. 7 - Prob. 31SGR Ch. 7 - Prob. 32SGR Ch. 7 - Prob. 33SGR Ch. 7 - Prob. 34SGR Ch. 7 - Prob. 35SGR Ch. 7 - Prob. 1PT Ch. 7 - Prob. 2PT Ch. 7 - Prob. 3PT Ch. 7 - Prob. 4PT Ch. 7 - Prob. 5PT Ch. 7 - Prob. 6PT Ch. 7 - Prob. 7PT Ch. 7 - Prob. 8PT Ch. 7 - Prob. 9PT Ch. 7 - Prob. 10PT Ch. 7 - Prob. 11PT Ch. 7 - Prob. 12PT Ch. 7 - Prob. 13PT Ch. 7 - Prob. 14PT Ch. 7 - Prob. 15PT Ch. 7 - Prob. 16PT Ch. 7 - Prob. 17PT Ch. 7 - Prob. 1STP Ch. 7 - Prob. 2STP Ch. 7 - Prob. 3STP Ch. 7 - Prob. 4STP Ch. 7 - Prob. 5STP Ch. 7 - Prob. 6STP Ch. 7 - Prob. 7STP Ch. 7 - Prob. 8STP Ch. 7 - Prob. 9STP Ch. 7 - Prob. 10STP Ch. 7 - Prob. 11STP Ch. 7 - Prob. 12STP Ch. 7 - Prob. 13STP Ch. 7 - Prob. 14STP Ch. 7 - Prob. 15STP

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