7/8 = 14/16
14/16 + 9/16 = 23/16
Answer:
![\triangle FED\sim \triangle JEH](https://tex.z-dn.net/?f=%5Ctriangle%20FED%5Csim%20%5Ctriangle%20JEH)
Step-by-step explanation:
Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity. ![\implies \boxed{\triangle FED\sim \triangle JEH}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7B%5Ctriangle%20FED%5Csim%20%5Ctriangle%20JEH%7D)
Since we know that dilation of a figure changes all sides of a figure by same factor.
Let us find out factor of dilation of our figure.
We will find side length QR of our quadrilateral QRST and its corresponding side QR' of quadrilateral Q'R'S'T'.
![\text{Length of QR}=5--1](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20QR%7D%3D5--1)
![\text{Length of QR}=5+1=6](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20QR%7D%3D5%2B1%3D6)
Let us find side length of Q'R'.
![\text{Length of Q'R'}=1--1](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20Q%27R%27%7D%3D1--1)
![\text{Length of Q'R'}=1+1=2](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20Q%27R%27%7D%3D1%2B1%3D2)
Let us compare both our side lengths to find factor of dilation,
![\frac{QR}{Q'R'}= \frac{6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BQ%27R%27%7D%3D%20%5Cfrac%7B6%7D%7B2%7D)
![\frac{QR}{Q'R'}= 3](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BQ%27R%27%7D%3D%203)
Upon cross multiplication we will get,
![QR=3\cdot Q'R'](https://tex.z-dn.net/?f=QR%3D3%5Ccdot%20Q%27R%27)
![Q'R'=\frac{1}{3} \cdot QR](https://tex.z-dn.net/?f=Q%27R%27%3D%5Cfrac%7B1%7D%7B3%7D%20%5Ccdot%20QR)
We can see that Q'R' is
of Q'R'. Therefore, our factor of dilation is
.
Answer 2 and 1/2 plotted 2 times 1 and 1/2 one time
2 and 3/4 four times 3 and 3/4 once 3 and 1/2 twice and 3 twice. Step-by-step explanation: