Chapter 4: Q6CE. (page 155)

Complete.
Refer to $Δ A B C$ and name each of the following.
a. a median of $Δ A B C$
b. an altitude of $Δ A B C$
c. a bisector of an angle of $Δ A B C$

Short Answer

Expert verified

a. $\bar{B E}$ is a median of $Δ A B C$

b. $\bar{A D}$ is an altitude of $Δ A B C$

c. $\bar{C F}$ is a bisector of an angle of $Δ A B C$

Step by step solution

Part a. Step 1. Observations from the figure.

$\bar{A E} ≅ \bar{C E} m ∠ A D C = 90 ° ∠ A C F ≅ ∠ B C F$

Part a. Step 2. Definition of median.

Median divides the triangle into two equal triangles and a side into two equal sides.

Part a. Step 3. Find median.

From observations $\bar{A E} ≅ \bar{C E}$ which means $\bar{B E}$ divides aside into two equal sides.

So, $\bar{B E}$ is a median of $Δ A B C$

Part b. Step 1. Observations from the figure.

$\bar{A E} ≅ \bar{C E} m ∠ A D C = 90 ° ∠ A C F ≅ ∠ B C F$

Part b. Step 2. Definition of altitude.

An altitude is a line that makes an angle of 90 degrees with the side of a triangle.

Part b. Step 3. Find altitude.

From observations $m ∠ A D C = 90 °$

So, $\bar{A D}$ is an altitude of $Δ A B C$

Part c. Step 1. Observations from the figure.

$\bar{A E} ≅ \bar{C E} m ∠ A D C = 90 ° ∠ A C F ≅ ∠ B C F$

Part c. Step 2. Definition of bisector of an angle.

An angle bisector is a line that divides an angle into two equal parts.

Part c. Step 3. Find median.

From observations $\bar{C F}$ dives the angles $∠ A C F and ∠ B C F$ into two equal parts.

So, $\bar{C F}$ is a bisector of an angle of $Δ A B C$

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Complete.
Refer to $Δ A B C$ and name each of the following.
a. a median of $Δ A B C$
b. an altitude of $Δ A B C$
c. a bisector of an angle of $Δ A B C$

Short Answer

Step by step solution

Part a. Step 1. Observations from the figure.

Part a. Step 2. Definition of median.

Part a. Step 3. Find median.

Part b. Step 1. Observations from the figure.

Part b. Step 2. Definition of altitude.

Part b. Step 3. Find altitude.

Part c. Step 1. Observations from the figure.

Part c. Step 2. Definition of bisector of an angle.

Part c. Step 3. Find median.

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Complete.Refer to ΔABCand name each of the following.a. a median ofΔABCb. an altitude ofΔABCc. a bisector of an angle of ΔABC

Short Answer

Step by step solution

Part a. Step 1. Observations from the figure.

Part a. Step 2. Definition of median.

Part a. Step 3. Find median.

Part b. Step 1. Observations from the figure.

Part b. Step 2. Definition of altitude.

Part b. Step 3. Find altitude.

Part c. Step 1. Observations from the figure.

Part c. Step 2. Definition of bisector of an angle.

Part c. Step 3. Find median.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

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Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Complete.
Refer to $Δ A B C$ and name each of the following.
a. a median of $Δ A B C$
b. an altitude of $Δ A B C$
c. a bisector of an angle of $Δ A B C$