Q8CE. Given: 螖DEF聽is isosceles with ... [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 4: Q8CE. (page 155)

Given: $螖 D E F$ is isosceles with $D F = E F$ ; $\overset{炉}{F X}$ bisects $鈭� D F E$
a. Would the median drawn from $F$ to $\overset{炉}{D E}$ be the same segment as $\overset{炉}{F X}$ ?
b. Would the altitude be drawn from $F$ to $\overset{炉}{D E}$ be the same segment as $\overset{炉}{F X}$ ?

Short Answer

Expert verified

a. Yes, the median is drawn from $F$ to $\overset{炉}{D E}$ be the same segment as $\overset{炉}{F X}$

b. Yes, the altitude is drawn from $F$ to be $\overset{炉}{D E}$ the same segment as $\overset{炉}{F X}$

Step by step solution

Part a. Step 1. Show that ΔDFX≅ΔEFX

Statement	Reason
1. $\overset{炉}{F X} 鈮� \overset{炉}{F X}$	Common line segment
2. $鈭� D F X 鈮� 鈭� E F X$	Given
3. $\overset{炉}{D F} 鈮� \overset{炉}{E F}$	Given
4. $螖 D F X 鈮� 螖 E F X$	SAS (Side-Angle-Side)Postulate

Part a. Step 2. Show that DX¯≅EX¯

Since corresponding parts of the congruent triangle are congruent

So, $\overset{炉}{D X} 鈮� \overset{炉}{E X}$

Part a. Step 3. Show that FX¯ is a median

Since $\overset{炉}{D X} 鈮� \overset{炉}{E X}$ , so $X$ is a midpoint of $\overset{炉}{D E}$

So, $\overset{炉}{F X}$ is the median.

Thus, the median drawn from $F$ to $\overset{炉}{D E}$ is the segment $\overset{炉}{F X}$

Part b. Step 1. Show that ΔDFX≅ΔEFX

Statement	Reason
1. $\overset{炉}{F X} 鈮� \overset{炉}{F X}$	Common line segment
2. $鈭� D F X 鈮� 鈭� E F X$	Given
3. $\overset{炉}{D F} 鈮� \overset{炉}{E F}$	Given
4. $螖 D F X 鈮� 螖 E F X$	SAS (Side-Angle-Side)Postulate

Part b. Step 2. Show that ∠FXD≅∠FXE

Since, corresponding parts of the congruent triangle are congruent

So, $鈭� F X D 鈮� 鈭� F X E$

Part b. Step 3. Show that FX¯ is an altitude

Since $鈭� F X D and 鈭� F X E$ forms a linear pair

Also, $鈭� F X D 鈮� 鈭� F X E$

$m 鈭� F X D + m 鈭� F X E = 180 掳 2 m 鈭� F X D = 180 掳 m 鈭� F X D = 90 掳$

So, $\overset{炉}{F X}$ is the altitude

Thus, the altitude drawn from F to $\overset{炉}{D E}$ is the segment $\overset{炉}{F X}$

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Short Answer

Step by step solution

Part a. Step 1. Show that ΔDFX≅ΔEFX

Part a. Step 2. Show that DX¯≅EX¯

Part a. Step 3. Show that FX¯ is a median

Part b. Step 1. Show that ΔDFX≅ΔEFX

Part b. Step 2. Show that ∠FXD≅∠FXE

Part b. Step 3. Show that FX¯ is an altitude

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91影视

Given: 螖DEFis isosceles with DF=EF; FX炉bisects鈭�DFEa. Would the median drawn from Fto DE炉 be the same segment as FX炉?b. Would the altitude be drawn from Fto DE炉 be the same segment as FX炉?

Short Answer

Step by step solution

Part a. Step 1. Show that ΔDFX≅ΔEFX

Part a. Step 2. Show that DX¯≅EX¯

Part a. Step 3. Show that FX¯ is a median

Part b. Step 1. Show that ΔDFX≅ΔEFX

Part b. Step 2. Show that ∠FXD≅∠FXE

Part b. Step 3. Show that FX¯ is an altitude

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Statistics

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.