If DE is the midsegment of ABC what is the value of x AND y?

3.) x = 4.5

4.) y = 7

Step-by-step explanation:

3 is an easier one than 4. By the triangle midsegment theorem, the midsegment of a triangle will be half of the base if it is parallel to it. AB is our base, so the equation is like this!

Now for 4, it actually is pretty easy. By the same triangle midsegment theorem, we automatically know that EC and EA are congruent, and CD and DB are also congruent. Meaning y equals 7.

But another way we can determine this (the long, kinda unecessary, but useful way) is through examining the relationship that triangles ABC and EDC have!  We know that they are similar triangles by SAS or AA. Meaning, their equation looks something like this...

Like I said earlier, 7 is equal to y, but I figured I'd prove it so we are on the same page. Nothing wrong with double-checking ;)

Have a nice day. Feel free to Ask questions. Spread The Love.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it