Mathematics, 19.07.2019 11:00 angelb2472

Which postulate or theorem, if any, could be used to prove the triangles congruent? if not enough information is given, write not enough information.

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Two triangles are congruent if and only if they have the same shape and size. So, there are several ways to find out if two triangles are congruent, so we will study the triangles above to find the answers:

Case a. (AAS - Angle, Angle, Side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal. So, for the figure above it is true that:

$\overline{AC}=\overline{DF}$
∠B = ∠E
∠A = ∠D

Case b. We don't have any information about this case that allows us to get a conclusion about congruence. Recall that for congruent triangles you need to compare three elements two by two.

Case c. (SSS - Side, Side, Side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. So, for the figure:

$\overline{AB}=\overline{ED}$
$\overline{AC}=\overline{DF}$
$\overline{BC}=\overline{EF}$

Case d. We only have two equal elements, but it is necessary to have three elements for comparing them doing the comparison two by two. There is not enough information for getting a conclusion.

Answer from: Quest

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step-by-step explanati∵∵∴∴on:

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is