1.in triangle trs, vz = 6 inches. what is rz? a.3 inches b.6 inches c.12 inches d.18 inches not b. 2.which statements regarding the diagram of δebc are true? check all that apply. a.∠bec is an exterior angle. b.∠dec is an exterior angle. c.∠abe and ∠ebc are supplementary angles. d.∠bcf and ∠bec are supplementary angles. e.∠bec is a remote interior angle to exterior f.∠bcf.

Part 1)

we know that

The Centroid of a Triangle is the centre of the triangle that can be calculated as the point of intersection of all the three medians of a triangle.

The Centroid divides each median into two segments whose lengths are in the ratio

so

we have

substitute

Find RZ

therefore

the answer Part 1) is the option C

Part 2)

Statements

case A) ∠BEC is an exterior angle

The statement is False

Because, ∠BEC is a internal angle

case B) ∠DEC is an exterior angle.

we know that

An exterior angle is formed by one side of a triangle and the extension of another side

therefore

The statement is True

case C) ∠ABE and ∠EBC are supplementary angles.

we know that

∠ABE+∠EBC= -------> by supplementary angles

therefore

The statement is True

case D) ∠BCF and ∠BEC are supplementary angles  

The statement is False

Because

the only way that is true is that the triangle BEC is isosceles and that the ∠BEC is equal to the ∠BCE  

case E) ∠BEC is a remote interior angle to exterior F.∠BCF

we know that

Remote interior angles are the interior angles of a triangle that are not adjacent to a given angle. Each interior angle of a triangle has two remote exterior angles.

In this problem  ∠BEC has two remote exterior angles (∠BCF and ∠EBA)

therefore

The statement is True

answer:  

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step-by-step explanation: easy