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Shkiper50 [21]
3 years ago
5

1.In triangle TRS, VZ = 6 inches. What is RZ?

Mathematics
2 answers:
Hunter-Best [27]3 years ago
4 0
1. C
2. B,C,E

Hope that helps.
Sergio [31]3 years ago
3 0

<u>Part 1) </u>

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=\frac{1}{3}RV

RV=3VZ

we have

VZ=6\ in

substitute

RV=3*6=18\ in

Find RZ

RZ=\frac{2}{3}RV

RZ=\frac{2}{3}*18=12\ in

therefore

<u>the answer Part 1) is the option C</u>

12\ in

<u>Part 2) </u>

Statements

<u>case A)</u> ∠BEC is an exterior angle

The statement is False

Because, ∠BEC is a internal angle

<u>case B</u>) ∠DEC is an exterior angle.

we know that

An <u>exterior angle</u> is formed by one side of a triangle and the extension of another side

therefore

The statement is True

<u>case C)</u> ∠ABE and ∠EBC are supplementary angles.

we know that

∠ABE+∠EBC=180\° -------> by supplementary angles

therefore

The statement is True

<u>case D) </u>∠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  

<u>case E)</u> ∠BEC is a remote interior angle to exterior F.∠BCF

we know that

<u>Remote interior angles</u> 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




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