In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :

Mathematics

1 answer:

Grace [21]3 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

$\angle DIH\cong \angle EGH$ as alternate interior angles;
$\angle DHI\cong \angle GHE$ as vertical angles;
$DH\cong HE$ because point H bisects segment DE (given).

Thus,

$\triangle DIH\cong \triangle EGH$ by AAS postulate

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Answer:
CD = x = 4 units

Explanation:
We are given that the two triangles are similar. This means that we can set the similarity proportionality as follows:
$\frac{BC}{CD} = \frac{CA}{CE} = \frac{AB}{ED}$

W e have:
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Substitute in the above proportionality and solve for x as follows:
$\frac{20-x}{x} = \frac{20}{5} = 4$

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5x = 20
x = 4

Based on he above:
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