Question

just the linked questions, thanks . 8.4 similar triangles unit 8 practice a

Answer 1

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. $\overline {ST}$ is parallel to $\overline{PR}$

9. $\overline{ST}$ is parallel to $\overline{PR}$

10. $\overline{ST}$ is not parallel to $\overline{PR}$

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

What is Thales theorem?

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment $\overline{ST}$ divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, $\overline{ST}$ ║ $\overline{PR}$

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, $\overline{ST}$ and $\overline{PR}$ bisects $\overline{QP}$ and $\overline{QR}$ into equal proportions and therefore, $\overline{ST}$ ║ $\overline{PR}$

10. The ratio of the sides the segment $\overline{ST}$  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore $\overline{ST}$ ∦ $\overline{PR}$

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

Learn more about Thales theorem here:

https://brainly.com/question/14417137

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