Chapter 6: Q4. (page 218)

Classify the following conditional as true or false.
If $∠ B C D$ is an exterior angle of $Δ A B C$ , then $m ∠ B C D > m ∠ A + m ∠ B$ .

Short Answer

Expert verified

The statement is false.

Step by step solution

Step 1. Apply the concept of the conditional statement.

Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also known as an " If-then" statement.

Step 2. Step description.

Consider the statement “if $∠ B C D$ is an exterior angle of $Δ A B C$ then $m ∠ B C D > m ∠ A + m ∠ B$ .”

Here $∠ B C D$ is an exterior angle of $Δ A B C$ .

From properties of triangle, measure of exterior angle is equal to the measure of sum of two opposite interior angles.

Step 3. Step description.

Since the measure of exterior angle is equal to the measure of sum of two opposite interior angles but here measure of exterior angle is greater than the sum of two interior angles such that $m ∠ B C D > m ∠ A + m ∠ B$ , which is not possible.

Therefore, the statement is false.

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Classify the following conditional as true or false.
If $∠ B C D$ is an exterior angle of $Δ A B C$ , then $m ∠ B C D > m ∠ A + m ∠ B$ .

Short Answer

Step by step solution

Step 1. Apply the concept of the conditional statement.

Step 2. Step description.

Step 3. Step description.

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Classify the following conditional as true or false.If ∠BCDis an exterior angle of ΔABC, then m∠BCD>m∠A+m∠B.

Short Answer

Step by step solution

Step 1. Apply the concept of the conditional statement.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Classify the following conditional as true or false.
If $∠ B C D$ is an exterior angle of $Δ A B C$ , then $m ∠ B C D > m ∠ A + m ∠ B$ .