Question

Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length of X Z is 18, the length of C Y is 25, and the length of Y D is 20. Lines C D and X Z are parallel. If and CX = 5 units, what is DZ? 2 units 3 units 4 units 5 units

Answer 1

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

∴ $\frac{YC}{YX}=\frac{CD}{XZ}=\frac{YD}{YZ}$

∵ 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

∵ $\frac{YC}{YX}=\frac{YD}{YZ}$

∴ $\frac{25}{30}=\frac{20}{20+DZ}$

- Simplify $\frac{25}{30}$ by dividing up and down by 5

∵ $\frac{25}{30}=\frac{5}{6}$

∴ $\frac{5}{6}=\frac{20}{20+DZ}$

- 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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