Answer: 5
Step-by-step explanation:
Answer: SAS similarity theorem
<u>Proportional relationship</u>:
![\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7BAB%7D%7BAC%7D%20%20%3D%20%5Cdfrac%7BAM%7D%7BAN%7D)
<u>insert values</u>
![\rightarrow \sf \dfrac{21+9}{14+6} = \dfrac{21}{14}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20%5Cdfrac%7B21%2B9%7D%7B14%2B6%7D%20%20%3D%20%5Cdfrac%7B21%7D%7B14%7D)
<u>simplify</u>
![\rightarrow \sf 1 = 1](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%201%20%3D%201)
L.H.S = R.H.S
The triangles are congruent and follows the rule SAS similarity theorem.
The triangles has/starts from the same angle, corner (A).
Let x represent the amount of sugar needed to make one batch of cookies.
We have been given that Pia used
of her sugar to make
of a batch of cookies. We are asked to find the amount of sugar needed to make whole batch.
We can represent our given information in an equation as:
![\frac{3}{4}x=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7Dx%3D%5Cfrac%7B2%7D%7B3%7D)
Let us solve for x.
![\frac{4}{3}\cdot \frac{3}{4}x=\frac{4}{3}\cdot \frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cfrac%7B3%7D%7B4%7Dx%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cfrac%7B2%7D%7B3%7D)
![x=\frac{4\cdot 2}{3\cdot 3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Ccdot%202%7D%7B3%5Ccdot%203%7D)
![x=\frac{8}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%7D%7B9%7D)
Therefore, Pia needs
of her sugar to make 1 whole batch of cookies.