StatementReason m∠ADE = 36°Given
m∠DAE = 90°Definition of a right angle
m∠AED = 54°Triangle Sum Theorem
segment DE joins the midpoints of segment AB and segment ACGiven
segment DE is parallel to segment BC?
∠ECB ≅ ∠AEDCorresponding angles are congruent
m∠ECB = 54°Substitution property

Which theorem can be used to fill in the missing reason?
Concurrency of Medians Theorem
Isosceles Triangle Theorem
Midsegment of a Triangle Theorem
Triangle Inequality Theorem

Midsegment of a Triangle Theorem

Step-by-step explanation:

Midsegment of a Triangle Theorem can be used to fill in the missing reason.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32