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The length of DZ is 4 units ⇒ 3rd answer
Step-by-step explanation:
Triangle X Y Z is cut by line segment C D, where
- C lies on side XY and D lies on the side YZ
- The length of C D is 15
- The length of X Z is 18
- The length of C Y is 25
- The length of Y D is 20
- C D and X Z are parallel
- CX = 5 units
We need to find the length of DZ
In Δ XYZ
∵ C ∈ XY and D ∈ YZ
∵ CD // XZ
∴ m∠YCD = m∠YXZ ⇒ alternate angles
∴ m∠YDC = m∠YZX ⇒ alternate angles
In Δs YCD and YXZ
∵ m∠YCD = m∠YXZ
∵ m∠YDC = m∠YZX
∵ ∠Y is a common angle
∴ Δ YCD is similar to Δ YXZ by AAA postulate
- There is a constant ratio between their corresponding sides
∴
∵ YC = 25 units
∵ CX = 5 units
∵ YX = YC + CX
∴ YX = 25 + 5 = 30 units
∵ YD = 20 units
∵ YZ = YD + DZ
∴ YZ = 20 + DZ
Let us use the ratio of the corresponding side
∵
∴
- Simplify by dividing up and down by 5
∵
∴
- By using cross multiplication
∴ 5(20 + DZ) = 6(20)
∴ 100 + 5 DZ = 120
- Subtract 100 from both sides
∴ 5 DZ = 20
- Divide both sides by 5
∴ DZ = 4 units
The length of DZ is 4 units
Learn more:
You can learn more about triangles in brainly.com/question/3202836
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