Question

I need help with geometry. Find x.

Answer 1

Answer:

Part 9) $x=5$  

Part 10) $x=-9$  

Step-by-step 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

Part 9) we know that

Point Q is the midpoint segment XY (QY=QX)

Point R is the midpoint segment XW (RW=RX)

Applying the Midpoint Theorem

RQ is parallel to WY

and

$RQ=\frac{1}{2}WY$  

we have

$RQ=2x-3\\WY=x+9$

substitute

$2x-3=\frac{1}{2}(x+9)$  

solve for x                  

$4x-6=(x+9)$          

$4x-x=9+6$

$3x=15$  

$x=5$  

Part 10) we know that

Point B is the midpoint segment TS (BS=BT)

Point C is the midpoint segment RS (CS=CR)

Applying the Midpoint Theorem

BC is parallel to TR

and

$BC=\frac{1}{2}TR$  

we have

$BC=x+19\\TR=x+29$

substitute

$x+19=\frac{1}{2}(x+29)$  

solve for x

$2x+38=(x+29)$  

$2x-x=29-38$          

$x=-9$