1. First, we can identify the equal angles based on their position within the shape:
\(∠MCD = ∠KCM\)
\(∠A = ∠DCE\)
\(△ABE = △CDE\)
We can also determine the value of \(x\) using the Pythagorean Theorem. This will allow us to determine the ratio of the 2 triangles within the shape:
\(a^2 + b^2 = c^2\)
\(x^2 + 9^2 = 20.1^2\)
\(x^2 = 404.01 - 81\)
`sqrt(x^2)` \(=\) `sqrt(323.01)`
\(x = 17.97 -> 18\)
We can now determine the ratios with \(x\) as the opposite side of the small triangle and the adjacent side of the large triangle:
ratio1: \(\cfrac{9}{18} = \cfrac{1}{2}\)
ratio2: \(\cfrac{18}{36} = \cfrac{1}{2}\)
Therefore, we can determine that △MCD = △KCM as they share a common angle and common ratio.
2. We can now identify the corresponding angles:
\(∠D = ∠KMC\)
\(∠DCM = ∠MCK\)
\(∠CMD = ∠K\)
\(\cfrac{MC}{KC} = \cfrac{CD}{CM} = \cfrac{MD}{KM}\)