Chapter 2: Q18 (page 68)

Name the definition or state the theorem that justifies the statement about the diagram.
If $\overset{\leftrightarrow}{NM} ⊥ \overset{\leftrightarrow}{GH}$ , then $∠ 3$ and $∠ 4$ complementary.

Short Answer

Expert verified

The statement regarding the diagram can justified by the Definition of perpendicular lines.

Step by step solution

Step 1. Observe the diagram.

Here, $\overset{\leftrightarrow}{N M} ⊥ \overset{\leftrightarrow}{G H}$ .

Step 2. State the definition of perpendicular lines.

The angle formed by two perpendicular lines is congruent adjacent angle.

Step 3. State the conclusion.

Considering the diagram and as $\overset{\leftrightarrow}{N M} ⊥ \overset{\leftrightarrow}{G H}$ , then $∠ M N H = 90^{\circ}$ and $∠ M N K = ∠ M N H$ as perpendicular lines make an angle of $90^{\circ}$ .

So, $∠ 3$ and $∠ 4$ are complimentary.

Therefore, the statement is justified by the definition of perpendicular lines.

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Name the definition or state the theorem that justifies the statement about the diagram.
If $\overset{\leftrightarrow}{NM} ⊥ \overset{\leftrightarrow}{GH}$ , then $∠ 3$ and $∠ 4$ complementary.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. State the definition of perpendicular lines.

Step 3. State the conclusion.

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Name the definition or state the theorem that justifies the statement about the diagram.If NM↔⊥GH↔, then∠3and∠4complementary.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. State the definition of perpendicular lines.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Statistics

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Study anywhere. Anytime. Across all devices.

Name the definition or state the theorem that justifies the statement about the diagram.
If $\overset{\leftrightarrow}{NM} ⊥ \overset{\leftrightarrow}{GH}$ , then $∠ 3$ and $∠ 4$ complementary.