Check the picture attached.
Let m(BAE)=m(ACD)=α
(BAE and ACD are congruent, since they are alternate interior angles, or Z angles)
Let m(ABE)=β.
So in triangle ABE, the measures of the angles are 90, α and β degrees.
This means that m(BCE)=β, since the 2 other angles of triangle BCE are 90 and α degrees.
thus, we have the similarity of triangles ABE and BCE,
so the following rations are equal:

so

so



(inches)
Remark, we can also apply Euclid's theorem directly.
Answer:
3
Step-by-step explanation:
The scale factor of ABC to DEF is the number you need to multiply a corresponding side of ABC to get one of DBC. We are given the two triangles are similar, so we can say that sides AB and DE are proportional. We are looking for the number we need to multiply AB by to get DE. From this relation, we can get the equation:
AB * x = DE
where x is our scale factor. We can substitute in the values of AB and DE, and solve for x:
5x = 15
x = 3
Therefore, the scale factor is three. This means that you can multiply any side of ABC by 3 to get a side of DEF.
-8 - 7x = -5x - 10....add 10 to both sides
2 - 7x = -5x ......NEXT STEP.....add 7x to both sides
390/6=65
65x10+650
650 is your answer
hope this helps
Answer
3. 14
4. 4
5. 8
Step-by-step explanation: