Solved: "Write a two-column proof. Given: MN―=∼MP―,NO―=∼PO― Prove: ∠N=∼∠P"

Elleanor Mckenzie

Answered question

2020-11-12

Write a two-column proof.
Given:

\overset{―}{M N} \tilde{=} \overset{―}{M P}, \overset{―}{N O} \tilde{=} \overset{―}{P O}

Prove:

∠ N \tilde{=} ∠ P

Answer & Explanation

saiyansruleA

Skilled2020-11-13Added 110 answers

Step 1
Given:

\overset{―}{M N} \tilde{=} \overset{―}{M P}, \overset{―}{N O} \tilde{=} \overset{―}{P O}

To prove:

∠ N \tilde{=} ∠ P

Step 2
Thus, The reflexive property of congruence,

\overset{―}{M O} \tilde{=} \overset{―}{M O}

Now Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.
By SSS congruence,

△ M N O \tilde{=} △ M P O

Corresponding parts of congruent triangle (CPCT).
Their corresponding sides are equal and angles are equal.
Therefore,

∠ N \tilde{=} ∠ P

2021-12-13

Answer:

$\begin{array}{cc} Statements & Reasons \\ 1) \overset{―}{M N} ≅ \overset{―}{M P}, \overset{―}{N O} ≅ \overset{―}{P O} & 1) Given \\ 2) \overset{―}{M O} ≅ \overset{―}{M O} & 2) Reflexive property \\ 3) △ M N O ≅ △ M P O & 3) SSS \\ 4) ∠ N ≅ ∠ P & 4) CPCTC \end{array}$

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