Chapter 3: Q7 (page 96)

Explain how each corollary of Theorem 3-11 follows from the theorem
Corollary 3

Short Answer

Expert verified

It is concluded that in a triangle there can be at most one right angle or obtuse angle.

Step by step solution

Step 1. State Theorem 3-11

Theorem 3-11 states that the sum of the angles is $180^{0}$ .

Step 2. Statement of corollary 3

Corollary 3 states that in a triangle there can be at most one right angle or obtuse angle.

Step 3. Consider a triangle with obtuse angle

Consider an obtuse triangle $Δ A B C$ such that:.

$\begin{matrix} ∠ A = 25 ° \\ ∠ B = 120 ° \\ ∠ C = 35 ° \end{matrix} ∠ A + ∠ B + ∠ C = 180 °$

Here, if two angles of a triangle would have been obtuse, the sum of the angles will be more than $180 °$ .

Step 4. Consider a triangle with right angle

Consider a triangle $Δ P Q R$ such that it has two right angles:

$\begin{matrix} ∠ P = 90 ° \\ ∠ Q = 90 ° \\ ∠ R = 0 ° \end{matrix} ∠ P + ∠ Q + ∠ R = 180 °$

Here, it is not possible in a triangle because the sum of three angles of a triangle is $180 °$ .

Thus, it can be concluded that in a triangle there can be at most one right angle or obtuse angle.

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Explain how each corollary of Theorem 3-11 follows from the theorem
Corollary 3

Short Answer

Step by step solution

Step 1. State Theorem 3-11

Step 2. Statement of corollary 3

Step 3. Consider a triangle with obtuse angle

Step 4. Consider a triangle with right angle

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Explain how each corollary of Theorem 3-11 follows from the theoremCorollary 3

Short Answer

Step by step solution

Step 1. State Theorem 3-11

Step 2. Statement of corollary 3

Step 3. Consider a triangle with obtuse angle

Step 4. Consider a triangle with right angle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Explain how each corollary of Theorem 3-11 follows from the theorem
Corollary 3