Chapter 2: Q9. (page 62)

Describe your plan for proving the following. You don’t need to give all the details.
Given: $\bar{A C} ⊥ \bar{B C}$ ;∠3 is complementary to ∠1.
Prove: $∠ 3 ≅ ∠ 2$

Short Answer

Expert verified

It is proven that $∠ 3 ≅ ∠ 2$ .

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Definition of complementary angles.

The complementary angles are the angles whose sum is 90°.

Step 3. Write the proof of the statement ∠3≅∠2.

∠3 is complementary to∠1.

Therefore, the sum of the angles∠3 and∠1 is 90°.

That implies,

$∠ 3 + ∠ 1 = 90 ° (1)$

As $\bar{A C} ⊥ \bar{B C}$ , therefore the lines AC and BC are perpendicular and therefore by using the definition of the perpendicular lines the measure of the angle $∠ A C B = 90 °$ .

By using the angle addition postulate:

$∠ A C B = ∠ 1 + ∠ 2$ .

Now,

$\begin{matrix} ∠ A C B = 90 ° \\ ∠ 1 + ∠ 2 = 90 ° (2) \end{matrix}$

Subtract the equation (2) from (1).

$∠ 3 + ∠ 1 - (∠ 1 + ∠ 2) = 90 ° - 90 ° ∠ 3 + ∠ 1 - ∠ 1 - ∠ 2 = 0 ∠ 3 - ∠ 2 = 0 ∠ 3 = ∠ 2$

Therefore, $∠ 3 ≅ ∠ 2$ .

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Describe your plan for proving the following. You don’t need to give all the details.
Given: $\bar{A C} ⊥ \bar{B C}$ ;∠3 is complementary to ∠1.
Prove: $∠ 3 ≅ ∠ 2$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of complementary angles.

Step 3. Write the proof of the statement ∠3≅∠2.

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Describe your plan for proving the following. You don’t need to give all the details.Given: AC¯⊥BC¯;∠3 is complementary to ∠1.Prove: ∠3≅∠2

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of complementary angles.

Step 3. Write the proof of the statement ∠3≅∠2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Statistics

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Describe your plan for proving the following. You don’t need to give all the details.
Given: $\bar{A C} ⊥ \bar{B C}$ ;∠3 is complementary to ∠1.
Prove: $∠ 3 ≅ ∠ 2$