Question

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.

Answer 1

1. C
2. B,C,E

Hope that helps.

Answer 2

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
`2:1`

so

`VZ=(1)/(3)RV`

`RV=3VZ`

we have

`VZ=6\ in`

substitute

`RV=3*6=18\ in`

Find RZ

`RZ=(2)/(3)RV`

`RZ=(2)/(3)*18=12\ in`

therefore

the answer Part 1) is the option C

`12\ in`

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=
`180\°` -------> 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