Triangle ABC is 252 cm². Point D is the midpoint of segment BC. Point E is on segment AC such that AE = 1/3 AC. Point F is on segment AB such that BF = 1/4 AB. What is the area of the shade part?

Triangle ABC is 252 cm². Point D is the midpoint of segment BC. Point E is on segment AC such that

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clapoint2003p3chnu

01.03.2022

Mathematics

$\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC$

Step-by-step explanation:

Right triangle ABC is reflected over AC to form triangle AFC.

Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.

Reflection is a rigid transformation which preserves lengths and angles, then

$\triangle ABC\cong \triangle AFC$

Dilation is a transformation which maps the triangle into similar triangle, so

$\triangle AFC \sim \triangle DEC$

Thus,

$\triangle ABC \sim \triangle DEC$

Similar triangle have congruent corresponding angles, so

$\angle B\cong \angle E$

and proportional corresponding sides

$\dfrac{BC}{EC}=\dfrac{AB}{DE}=\dfrac{2}{3}\Rightarrow \\ \\3BC=2EC\\ \\3AB=2DE$

Thus, correct options are:

$\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC$

Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triang

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