Mathematics, 05.05.2020 17:05 arielpraczko1

Given: AB ≅ BC , m∠MOC = 135° OM − angle bisector Prove: ∠ABO ≅ ∠OBC

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Answer from: ranaawilliamsoowl6dk

Check attachment for the given triangle.

Proved

Step-by-step explanation:

Given m∠MOC = 135°

The sum of angles on a straight line is 180°, then

m∠MOC + m∠AOM = 180°

135° + m∠AOM = 180°

m∠AOM = 180° - 135° = 45°

Since OB bisects ∠AOC = 180°, they are perpendicular, and

∠AOB = 90°

Since OM bisects ∠AOB,

m∠AOM = m∠MOB = 45°

Since BO is perpendicular to AC m∠BOC = 90°

Triangle ABC is isosceles because AB ≅ BC.

BO bisects angle B , then

∠ABO ≅ ∠CBO

as required

Given: AB ≅ BC , m∠MOC = 135° OM − angle bisector Prove: ∠ABO ≅ ∠OBC

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