4) If C, P, and T are the midpoints of the sides of AAEN, PT = 13, EN = 43, and CP = 29,
find each measure.
a) AE =
E
N
b) AN =
T
c) CT =
d) Perimeter of
AAEN:
А

Answers:

Work Shown:

Because points C, P, and T are midpoints of the sides of triangle AEN, this means the segments CP, PT, and CT are midsegments of triangle AEN.

The segment PT = 13 is a midsegment of the larger triangle, and it is parallel to the side AE. Recall the midsegment is half as long as its parallel side.

This means,

PT = (1/2)*AE

2*PT = AE

AE = 2*PT

AE = 2*13

AE = 26

We'll use the same idea to find AN

CP = (1/2)*AN

2*CP = AN

AN = 2*CP

AN = 2*29

AN = 58

And we can also say,

CT = (1/2)*EN

CT = (1/2)*43

CT = 22.5

Add up the sides of triangle AEN to find its perimeter

Perimeter of triangle AEN = (AE)+(EN)+(AN)

Perimeter of triangle AEN = (26)+(43)+(58)

Perimeter of triangle AEN = 127

the correct answer is 5 6 and 7