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Given that π΄πΈπΉπ· is a parallelogram, where πΈ and πΉ are the midpoints of π·π΅ and π·πΆ, respectively, find the length of πΆπ΅.
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So our goal is to find the length of πΆπ΅.
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So letβs begin going through what weβre given.
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We are given that π΄πΈπΉπ· is a parallelogram.
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And we know that π·π΄ is 2.6 centimeters.
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Well, in a parallelogram, opposite sides are congruent.
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So that means πΉπΈ would also be 2.6 centimeters.
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Next, weβre given information about midpoints.
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πΈ is the midpoint of π·π΅.
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And F is the midpoint of π·πΆ.
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The length of a line segment joining the midpoints of two sides of a triangle is equal to half the length of the third side.
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So if we look at this triangle, triangle πΆπ·π΅, we are told the length of the line segment joining the two midpoints on the two sides of the triangle will be half of the length of the third side, side πΆπ΅.
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So πΉπΈ should be equal to half of πΆπ΅.
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Well, we know that πΉπΈ is equal to 2.6.
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So to solve for πΆπ΅, we can multiply both sides of the equation by two.
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And two times 2.6 is 5.2.
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Therefore, the length of πΆπ΅ will be equal to 5.2 centimeters.