Question

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

Answer 1

Answers are as follows: AE = 26

AN = 58

CT = 21.5 because half of 43 is equal to 21.5

Explanation:

The midsegment points are as follows: CT which is parallel to EN which measures 43 so half of 43 = 21.5 CT = 21.5

Midsegment CP is equal to 29. It is parallel to AN so you double it to get the measure for AN 29*2 = 58 AN = 58

Midsegment PT is equal to 13 and parallel to AE. You double 13 to get the

measure for AE, so 13 x 2 = 26 AE = 26

To get the perimeter of Angle AEN you add up all the sides of that angle.

so... 43+58+26 = 127 - the perimeter equals 127

Hope this helps!!

Answer 2

Answers:

• AE = 26
• AN = 58
• CT = 22.5
• Perimeter of triangle AEN = 127

=========================================================

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