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Dafna1 [17]
3 years ago
10

Select the statement that is missing from the proof below showing that vertical angles formed by intersecting lines are congruen

t.
Statements Reasons
1. ∠ABD and ∠ABC form a linear pair,∠CBE and ∠ABC form a linear pair 1. Definition of a linear pair
2. ∠ABD and ∠ABC are supplementary,∠CBE and ∠ABC are supplementary 2. Linear pair postulate
3. m∠ABD + m∠ABC = 180°,m∠CBE + m∠ABC = 180° 3. Definition of supplementary
4. ? 4. Substitution Property of Equality
5. m∠ABD = m∠CBE 5. Subtraction Property of Equality
6. ∠ABD≅∠CBE 6. Definition of congruent angles

m∠ABD+ m∠ABC = m∠DBC


m∠ABD+m∠DBE = m∠ABE

m∠ABD+m∠ABC=m∠DBE+m∠EBC

m∠ABD+ m∠ABC = m∠CBE + m∠ABC
Mathematics
1 answer:
bazaltina [42]3 years ago
5 0

No se su respuesta porque no intiendo en ingles

entonces vaya se ALV pinche puto marica

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The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.
MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =3\times\ side

3\times\ side =[tex]81\sqrt{3}

Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm

Thus from the diagram , Side AB=BC=AC= 27\sqrt{3} \ cm

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus \angle OBC = 30°

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2}  } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB}  \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

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