Chapter 3: Q45. (page 115)

Write a two-column proof.
Given: $\bar{WX} ⊥ \bar{XY}$ ;
∠1 is comp. to∠3.
Prove:∠2≅∠3.

Short Answer

Expert verified

The two-column proof to prove $∠ 2 ≅ ∠ 3$ is:

Statement	Reason
$∠ W X Y = 90 °$	Given
$‎ ∠ 1 + ∠ 2 = 90 °$	Angle addition postulate
$‎ ∠ 1 + ∠ 3 = 90 °$	Given

Step by step solution

Step 1. Consider the diagram.

Here, $\bar{W X} ⊥ \bar{X Y}$ and ∠1 complementary to ∠3.

Step 2. State the proof.

From the diagram and the information:

$∠ W X Y = 90 °$ ... (Given)

$∠ 1 + ∠ 2 = 90 °$ ... (Angle addition postulate).

$∠ 1 + ∠ 3 = 90 °$ ... (Given).

Thus, $∠ 2 ≅ ∠ 3$ .

Step 3. State the conclusion.

Therefore, the two-column proof is:

Statement	Reason
$∠ W X Y = 90 °$	Given
$‎ ∠ 1 + ∠ 2 = 90 °$	Angle addition postulate
$‎ ∠ 1 + ∠ 3 = 90 °$	Given

Hence,

∠ 2 ≅ ∠ 3

(proved).

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Write a two-column proof.
Given: $\bar{WX} ⊥ \bar{XY}$ ;
∠1 is comp. to∠3.
Prove:∠2≅∠3.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

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Write a two-column proof.Given: WX¯⊥XY¯; ∠1 is comp. to∠3.Prove:∠2≅∠3.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Write a two-column proof.
Given: $\bar{WX} ⊥ \bar{XY}$ ;
∠1 is comp. to∠3.
Prove:∠2≅∠3.