Question

Solve the problems. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.

Given: Quadrilateral AMNO
MN║AO
AM║ON
Prove: ∆AMN ≅ ∆NOA

Answer 1

∆AMN=∆NOA by rule SSS

Answer 2

∆AMN ≅ ∆NOA

Explanation:

Given:

Quadrilateral AMNO

MN║AO

AM║ON

To prove:∆AMN ≅ ∆NOA

Lets first draw two diagonals represented by lines MO and AN inside the given quadrilateral AMNO

Now we know if lines are parallel then the alternate interior angles are congruent , hence

∠NMO≅∠AOM

∠MNA≅∠NAO

∠AMO≅∠NOM

∠MAN≅∠ANO

Also by Reflexive Property we have

NA≅NA

MO≅MO

From ASA congruence property of triangles that states that if two angles and a side of two triangles are congruent then the two triangle are said to be congruent, hence we have

ΔAMN≅ΔNOA

ΔMAO≅ΔONM !