Q24 Draw 螖ABC and let D be the midp... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q24 (page 180)

Draw $螖 ABC$ and let D be the midpoint of $\overset{炉}{AB}$ . Let E be the midpoint of $\overset{炉}{CD}$ . Let F be the intersection of $\overset{鈫�}{AE}$ and $\overset{炉}{BC}$ . Draw $\overset{炉}{DG}$ parallel to $\overset{炉}{EF}$ meeting $\overset{炉}{BC}$ at G. Prove that $BG = GF = FC$ .

Short Answer

Expert verified

The diagram is:

The midpoint divides the segment into two congruent segments and Transitive Property proves $BG = GF = FC$ .

Step by step solution

Step 1. Consider the diagram.

The $螖 A B C$ is:

In $螖 A B C$ , D be the midpoint of $\overset{炉}{A B}$ . Let E be the midpoint of $\overset{炉}{C D}$ . Let F be the intersection of $\overset{鈫�}{A E}$ and $\overset{炉}{B C}$ . Draw $\overset{炉}{D G}$ parallel to $\overset{炉}{E F}$ meeting $\overset{炉}{B C}$ at G.

Step 2. State the transitive property.

The transitive property states that if $A = B$ and $B = C$ , then $A = C$ .

Step 3. Show the proof.

Statement	Reasons
In $螖 D G C$ , E is the midpoint of $\overset{炉}{C D}$ and $\overset{炉}{D G} 鈭� \overset{炉}{E F}$ .	Given.
F is the midpoint of $\overset{炉}{G C}$ .	A line that contains the midpoint of the side of a triangle and is parallel to another side passes through the midpoint of the third side.
$G F = F C$	Midpoint divides the segment into two congruent segments.
In $螖 A B F$ , D is the midpoint of $\overset{炉}{A B}$ and $\overset{炉}{D G} 鈭� \overset{炉}{A F}$	Given.
G is the midpoint of $\overset{炉}{B F}$ .	A line that contains the midpoint of the side of a triangle and is parallel to another side passes through the midpoint of the third side.
$B G = G F$	Midpoint divides the segment into two congruent segments.
$B G = G F = F C$	Transitive Property.

Step 4. State the conclusion.

Therefore, the statement $B G = G F = F C$ is proved by:

The midpoint divides the segment into two congruent segments that is $B G = G F = F C$

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91影视

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the transitive property.

Step 3. Show the proof.

Step 4. State the conclusion.

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91影视

Draw 螖ABC and let D be the midpoint of AB炉. Let E be the midpoint of CD炉. Let F be the intersection of AE鈫� and BC炉. DrawDG炉 parallel toEF炉 meetingBC炉 at G. Prove that BG=GF=FC .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the transitive property.

Step 3. Show the proof.

Step 4. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Logic and Functions

Geometry

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.