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High School Math Geometry Geometry, Student Edition

To prove: The length of line joining the midpoints of two sides of a triangle is equal to the one half the length of the third side.

To prove: The length of line joining the midpoints of two sides of a triangle is equal to the one half the length of the third side.

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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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 4.8, Problem 22PPS

To determine

To prove: The length of line joining the midpoints of two sides of a triangle is equal to the one half the length of the third side.

Expert Solution & Answer

Explanation of Solution

The figure can be drawn as:

Geometry, Student Edition, Chapter 4.8, Problem 22PPS

The coordinates of S will be:

$=(0+a2,0+h2)=(a2,h2)$

The coordinates of T will be:

$=(a+b2,0+h2)=(a+b2,h2)$

The length of BC will be:

$BC=(x2−x1)2+(y2−y1)2BC=(b−0)2+(0−h)2BC=b2+h2$

The length of AB will be:

$AB=(x2−x1)2+(y2−y1)2AB=(b−0)2+(0−0)2AB=b2+0AB=b$

The length of ST will be:

$ST=(x2−x1)2+(y2−y1)2ST=(a+b2−a2)2+(h2−h2)2ST=14b2+0ST=12bHence,ST=12(AB)$

Chapter 4.8, Problem 21PPS

Chapter 4.8, Problem 23PPS

Chapter 4 Solutions

Geometry, Student Edition

Ch. 4.1 - Prob. 1ACYP Ch. 4.1 - Prob. 1BCYP Ch. 4.1 - Prob. 2CYP Ch. 4.1 - Prob. 3CYP Ch. 4.1 - Prob. 4CYP Ch. 4.1 - Prob. 5CYP Ch. 4.1 - Prob. 1CYU Ch. 4.1 - Prob. 2CYU Ch. 4.1 - Prob. 3CYU Ch. 4.1 - Prob. 4CYU

Ch. 4.1 - Prob. 5CYU Ch. 4.1 - Prob. 6CYU Ch. 4.1 - Prob. 7CYU Ch. 4.1 - Prob. 8CYU Ch. 4.1 - Prob. 9CYU Ch. 4.1 - Prob. 10CYU Ch. 4.1 - Prob. 11CYU Ch. 4.1 - Prob. 12CYU Ch. 4.1 - Prob. 13CYU Ch. 4.1 - Prob. 14CYU Ch. 4.1 - Prob. 15PPS Ch. 4.1 - Prob. 16PPS Ch. 4.1 - Prob. 17PPS Ch. 4.1 - Prob. 18PPS Ch. 4.1 - Prob. 19PPS Ch. 4.1 - Prob. 20PPS Ch. 4.1 - Prob. 21PPS Ch. 4.1 - Prob. 22PPS Ch. 4.1 - Prob. 23PPS Ch. 4.1 - Prob. 24PPS Ch. 4.1 - Prob. 25PPS Ch. 4.1 - Prob. 26PPS Ch. 4.1 - Prob. 27PPS Ch. 4.1 - Prob. 28PPS Ch. 4.1 - Prob. 29PPS Ch. 4.1 - Prob. 30PPS Ch. 4.1 - Prob. 31PPS Ch. 4.1 - Prob. 32PPS Ch. 4.1 - Prob. 33PPS Ch. 4.1 - Prob. 34PPS Ch. 4.1 - Prob. 35PPS Ch. 4.1 - Prob. 36PPS Ch. 4.1 - Prob. 37PPS Ch. 4.1 - Prob. 38PPS Ch. 4.1 - Prob. 39PPS Ch. 4.1 - Prob. 40PPS Ch. 4.1 - Prob. 41PPS Ch. 4.1 - Prob. 42PPS Ch. 4.1 - Prob. 43PPS Ch. 4.1 - Prob. 44PPS Ch. 4.1 - Prob. 45PPS Ch. 4.1 - Prob. 46PPS Ch. 4.1 - Prob. 47PPS Ch. 4.1 - Prob. 48PPS Ch. 4.1 - Prob. 49PPS Ch. 4.1 - Prob. 50PPS Ch. 4.1 - 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