Chapter 4: Q.17 (page 165)

State whether the given information be used to prove that two lines are parallel and also state which lines.
Given: $\bar{MO} ⊥ \bar{NP}$ ; $\bar{NO} ≅ \bar{PO}$ .
Prove: $\bar{MN} ≅ \bar{MP}$ .

Short Answer

Expert verified

It is proved $\bar{N M} ≅ \bar{M P}$ .

Step by step solution

Step 1. Consider the diagram.

Here, $\bar{M O} ⊥ \bar{N P}$ and $N O ≅ P O$ .

Step 2. Show the calculation.

Consider the right angled $Δ N Q O$ and $Δ P Q O$ :

$\bar{N O} ≅ \bar{P O}$ , which are hypotenuse.

$\bar{Q O} ≅ \bar{Q O}$ , which are legs.

So, by HL Postulate, $Δ N Q O ≅ Δ P Q O$ .

So, $\bar{N Q} ≅ \bar{P Q}$ .

Consider $Δ N Q M$ and $Δ P Q M$ :

$\bar{N Q} ≅ \bar{P Q}$

$∠ N Q M ≅ ∠ P Q M = 90 °$

$\bar{Q M} ≅ \bar{Q M}$

So, by SAS Postulate, $Δ N Q M ≅ Δ P Q M$ .

So, $\bar{N M} ≅ \bar{M P}$

Step 3. State the conclusion.

Therefore, $\bar{N M} ≅ \bar{M P}$ (proved).

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State whether the given information be used to prove that two lines are parallel and also state which lines.
Given: $\bar{MO} ⊥ \bar{NP}$ ; $\bar{NO} ≅ \bar{PO}$ .
Prove: $\bar{MN} ≅ \bar{MP}$ .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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State whether the given information be used to prove that two lines are parallel and also state which lines.Given: MO¯⊥NP¯; NO¯≅PO¯. Prove: MN¯≅MP¯.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

State whether the given information be used to prove that two lines are parallel and also state which lines.
Given: $\bar{MO} ⊥ \bar{NP}$ ; $\bar{NO} ≅ \bar{PO}$ .
Prove: $\bar{MN} ≅ \bar{MP}$ .