1. Determine whether it is possible to form a triangle with side lengths 5, 7, and 8.
A. yes
B. no
5-Minute Check 1

2. Determine whether it is possible to form a triangle with side lengths 4.2, 4.2, and 8.4.
A. yes
B. no
5-Minute Check 2

3. Determine whether it is possible to form a triangle with side lengths 3, 6, and 10.
A. yes
B. no
5-Minute Check 3

4. Find the range for the measure of the third side of a triangle if two sides measure 4 and 13.
B. 6 < n < 16
C. 8 < n < 17
D. 9 < n < 17
5-Minute Check 4

5. Find the range for the measure of the third side of a triangle if two sides measure 8.3 and 15.6.
B. 9.1 < n < 22.7
C. 7.3 < n < 23.9
D. 6.3 < n < 18.4
5-Minute Check 5

6. Write an inequality to describe the length of MN.
___
A. 12 ≤ MN ≤ 19
B. 5 < MN < 19
C. 5 < MN < 12
D. 7 < MN < 12
5-Minute Check 6

7. Use proportional parts within triangles.
Use proportional parts with parallel lines.
Then/Now

8. Concept

9. Find the Length of a Side
Example 1

10. Substitute the known measures.
Find the Length of a Side
Substitute the known measures.
Cross Products Property
Multiply.
Divide each side by 8.
Simplify.
Example 1

11. A. 2.29 B
C. 12 D
Example 1

12. Concept

13. In order to show that we must show that
Determine if Lines are Parallel
In order to show that we must show that
Example 2

14. Since the sides are proportional.
Determine if Lines are Parallel
Since the sides are proportional.
Answer: Since the segments have proportional lengths, GH || FE.
Example 2

15. A. yes
B. no
C. cannot be determined
Example 2

16. Concept

17. A. In the figure, DE and EF are midsegments of ΔABC. Find AB.
Use the Triangle Midsegment Theorem
A. In the figure, DE and EF are midsegments of ΔABC. Find AB.
Example 3

18. ED = AB Triangle Midsegment Theorem 1 2 5 = AB Substitution 1 2
Use the Triangle Midsegment Theorem
ED = AB Triangle Midsegment Theorem __ 1 2
5 = AB Substitution __ 1 2
10 = AB Multiply each side by 2.
Answer: AB = 10
Example 3

19. B. In the figure, DE and EF are midsegments of ΔABC. Find FE.
Use the Triangle Midsegment Theorem
B. In the figure, DE and EF are midsegments of ΔABC. Find FE.
Example 3

20. FE = BC Triangle Midsegment Theorem
Use the Triangle Midsegment Theorem __ 1 2
FE = BC Triangle Midsegment Theorem
FE = (18) Substitution __ 1 2
FE = 9 Simplify.
Answer: FE = 9
Example 3

21. C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE.
Use the Triangle Midsegment Theorem
C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE.
Example 3

22. By the Triangle Midsegment Theorem, AB || ED.
Use the Triangle Midsegment Theorem
By the Triangle Midsegment Theorem, AB || ED.
AFE  FED Alternate Interior Angles Theorem
mAFE = mFED Definition of congruence
mAFE = 87 Substitution
Answer: mAFE = 87
Example 3

23. A. In the figure, DE and DF are midsegments of ΔABC. Find BC.
Example 3

24. B. In the figure, DE and DF are midsegments of ΔABC. Find DE.
Example 3

25. C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD.
Example 3

26. Concept

27. Use Proportional Segments of Transversals
MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.
Example 4

28. Triangle Proportionality Theorem
Use Proportional Segments of Transversals
Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.
Triangle Proportionality Theorem
Cross Products Property
Multiply.
Divide each side by 13.
Answer: x = 32
Example 4

29. In the figure, Davis, Broad, and Main Streets are all parallel
In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x.
A. 4
B. 5
C. 6
D. 7
Example 4

30. Concept

31. 2x – 7 = 5 Subtract x from each side. 2x = 12 Add 7 to each side.
Use Congruent Segments of Transversals
ALGEBRA Find x and y.
To find x:
3x – 7 = x + 5 Given
2x – 7 = 5 Subtract x from each side.
2x = 12 Add 7 to each side.
x = 6 Divide each side by 2.
Example 5

32. Use Congruent Segments of Transversals
To find y:
The segments with lengths 9y – 2 and 6y are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal.
Example 5

33. 9y – 2 = 6y + 4 Definition of congruence
Use Congruent Segments of Transversals
9y – 2 = 6y + 4 Definition of congruence
3y – 2 = 4 Subtract 6y from each side.
3y = 6 Add 2 to each side.
y = 2 Divide each side by 3.
Answer: x = 6; y = 2
Example 5

34. Find a and b.
A ;
B. 1; 2
C. 11;
D. 7; 3 __ 2 3
Example 5