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

∆AMN ≅ ∆NOA

Step-by-step 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  !

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be