In triangle XYZ, D and E are midpoints of XY and XZ. If YZ=1/2, find DE.
b.what other relationships exists between DE and YZ?
c.Name an angle congruent to angle XDE. Justify your answer.

Question

In triangle XYZ, D and E are midpoints of XY and XZ. If YZ=1/2, find DE.
b.what other relationships exists between DE and YZ?
c.Name an angle congruent to angle XDE. Justify your answer.

anonymous · Answer

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anonymous · Answer

So far, I have... a. DE=1.4 or 0.25 un.
b. _______________________
c. angle XYZ because of corresponding angles postulate OR is it theorem??

directrix · Answer

The solution lies in the application of two Geometry theorems. 
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The segment joining the midpoints of two sides of a triangle is equal to half that of the third side and is parallel to the third side.

a)  DE = 1/2(1/2) = 1/4

b) Seg DE is parallel to Seg YZ

If two parallel lines are cut by a transversal, corresponding angles are congruent.

c) angle XDE is congruent to angle XYZ