Chapter 4: Q.16 (page 165)

State whether the given information be used to prove that two lines are parallel and also state which lines.
Given: $\bar{MN} ≅ \bar{MP}$ ; $∠ NMO ≅ ∠ PMO$ .
Prove: $\overset{\leftrightarrow}{MO}$ is the $⊥$ bisector of $\bar{NP}$ .

Short Answer

Expert verified

$\overset{\leftrightarrow}{M O}$ is the perpendicular bisector of $\bar{N P}$ .

Step by step solution

Step 1. Consider the diagram.

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

Step 2. Show the calculation.

Consider the $Δ M N O$ and $Δ M P O$ :

$\bar{M N} ≅ \bar{M P}$

$∠ N M O ≅ ∠ P M O$

$\bar{M O} ≅ \bar{M O}$

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

So, $\bar{N O} ≅ \bar{P O}$ .

Hence, by Theorem 4-6, $\overset{\leftrightarrow}{M O}$ is the perpendicular bisector of $\bar{N P}$ .

Step 3. State the conclusion.

Therefore, $\overset{\leftrightarrow}{M O}$ is the perpendicular bisector of $\bar{N P}$ (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: $\bar{MN} ≅ \bar{MP}$ ; $∠ NMO ≅ ∠ PMO$ .
Prove: $\overset{\leftrightarrow}{MO}$ is the $⊥$ bisector of $\bar{NP}$ .

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: MN¯≅MP¯; ∠NMO≅∠PMO. Prove:MO↔is the ⊥bisector of NP¯.

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

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Probability and 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: $\bar{MN} ≅ \bar{MP}$ ; $∠ NMO ≅ ∠ PMO$ .
Prove: $\overset{\leftrightarrow}{MO}$ is the $⊥$ bisector of $\bar{NP}$ .