Congruent triangles have equal corresponding sides and angles.
- The measure of the side lengths are:
,
and ![\mathbf{GJ = 19m}](https://tex.z-dn.net/?f=%5Cmathbf%7BGJ%20%3D%2019m%7D)
- The measure of the angles are:
,
and ![\mathbf{\angle F = 105^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20F%20%3D%20105%5Eo%7D)
The given parameters are:
![\mathbf{\triangle D EF \cong \triangle GJH}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Ctriangle%20D%20EF%20%5Ccong%20%5Ctriangle%20GJH%7D)
![\mathbf{EF = 14m}](https://tex.z-dn.net/?f=%5Cmathbf%7BEF%20%3D%2014m%7D)
![\mathbf{D E = 19m}](https://tex.z-dn.net/?f=%5Cmathbf%7BD%20E%20%3D%2019m%7D)
![\mathbf{GH = 16m}](https://tex.z-dn.net/?f=%5Cmathbf%7BGH%20%3D%2016m%7D)
![\mathbf{\angle D = 34^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20D%20%3D%2034%5Eo%7D)
![\mathbf{\angle H = 105^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20H%20%3D%20105%5Eo%7D)
means that triangles DEF and GHJ are congruent triangles.
So, we have:
![\mathbf{DF = GH}](https://tex.z-dn.net/?f=%5Cmathbf%7BDF%20%3D%20GH%7D)
This gives
![\mathbf{DF = 16m}](https://tex.z-dn.net/?f=%5Cmathbf%7BDF%20%3D%2016m%7D)
Also, we have:
![\mathbf{JH = EF}](https://tex.z-dn.net/?f=%5Cmathbf%7BJH%20%3D%20EF%7D)
This gives
![\mathbf{JH = 14m}](https://tex.z-dn.net/?f=%5Cmathbf%7BJH%20%3D%2014m%7D)
Also, we have:
![\mathbf{GJ = DE}](https://tex.z-dn.net/?f=%5Cmathbf%7BGJ%20%3D%20DE%7D)
This gives
![\mathbf{GJ = 19m}](https://tex.z-dn.net/?f=%5Cmathbf%7BGJ%20%3D%2019m%7D)
The following angles are also congruent
![\mathbf{\angle F = \angle H}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20F%20%3D%20%5Cangle%20H%7D)
This gives
![\mathbf{\angle F = 105^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20F%20%3D%20105%5Eo%7D)
Also, we have:
![\mathbf{\angle G = \angle D}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20G%20%3D%20%5Cangle%20D%7D)
This gives
![\mathbf{\angle G = 34^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20G%20%3D%2034%5Eo%7D)
The measure of angle J is then calculated using
![\mathbf{\angle J + \angle H + \angle G = 180^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20J%20%2B%20%5Cangle%20H%20%2B%20%5Cangle%20G%20%3D%20180%5Eo%7D)
This gives
![\mathbf{\angle J + 105 + 34= 180^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20J%20%2B%20105%20%2B%2034%3D%20180%5Eo%7D)
![\mathbf{\angle J + 139= 180^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20J%20%2B%20139%3D%20180%5Eo%7D)
Subtract 139 from both sides
![\mathbf{\angle J = 41^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20J%20%3D%2041%5Eo%7D)
Read more about congruent triangles at:
brainly.com/question/4364353
The answer is c because it is a positive
It would serve 5.3 people, or just 5 because you can't have .3 of a person. This is because 9/4=12/x so 9x=48, and 48 divided by 9 is 5.3, or just 5 people.
The 250 cm board is cut into 5 pieces.
since three short pieces are of equal length, lets name each piece as 'x'
the longer ones are 15 cm longer than shorter ones so we can name them as 'x +15'
the sum of these pieces are 250
x + x + x + (x+15) + (x + 15) = 250
3x + 2x + 30 = 250
5x = 250 - 30
5x = 220
x = 44 cm
length of a short piece - 44 cm
length of long piece - 44 + 15 = 59 cm
Answer:
123.210,000
Step-by-step explanation:
one hundred and twenty-three million two hundred ten thousand