Question

Introduction to the triangle midsegment theorem‼️ can someone help me find BC,DE, and CE please ❓

Answer 1

Part 1)
`BC=68\ units`

Part 2)
`DE=36\ units`

Part 3)
`CE=34\ units`

Explanation:

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

so

Part 1) Find the length of BC

Applying the Midpoint Theorem

`DF=(1)/(2)BC`

we have

`DF=34\ units`

substitute the given value

`34=(1)/(2)BC`

solve for BC

`BC=34(2)=68\ units`

Part 2) Find the length of DE

Applying the Midpoint Theorem

`DE=(1)/(2)AC`

we have

`AC=72\ units`

substitute the given value

`DE=(1)/(2)(72)`

`DE=36\ units`

Part 3) Find the length of CE

we know that

`BC=CE+BE` ----> by addition segment postulate

The point E is the midpoint segment BC

That means

`CE=BE`

so

`BC=2CE`

we have

`BC=68\ units`

substitute

`68=2CE`

solve for CE

`CE=68/2`

`CE=34\ units`