Download g_5-5_inequalities

8. 𝐶
Homework: Page276, 277: 8, 11-16 all, 19-22 all, 28 a,b,c. 11. 𝑇𝑌 = 18, 𝑇𝑊 = 27
12. 𝑍𝑌 = 4.5, ZU = 13.5
13. 𝑉𝑌 = 6, 𝑌𝑋 = 3
14. 𝑀𝑒𝑑𝑖𝑎𝑛, 𝐴 𝑖𝑠 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡
15. 𝑁𝑒𝑖𝑡ℎ𝑒𝑟, 𝑖𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑎
𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑑𝑟𝑎𝑤𝑛 𝑓𝑟𝑜𝑚 𝑎
𝑣𝑒𝑟𝑡𝑒𝑥
16. 𝐴𝑙𝑡𝑖𝑡𝑢𝑑𝑒. 𝐴𝐵 𝑖𝑠 𝑎
𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑑𝑟𝑎𝑤𝑛 𝑓𝑟𝑜𝑚 𝑎 𝑣𝑒𝑟𝑡𝑒𝑥
𝑎𝑛𝑑 𝑖𝑠 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑡ℎ𝑒
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒.
Homework: Page276, 277: 8, 11-16 all, 19-22 all, 28 a,b,c.
19. 𝐵𝐸
20. 𝐹𝐶
21. 𝐶𝐴
22. 𝐷𝐺
28𝑎. 𝑎𝑛𝑔𝑙𝑒 𝑏𝑖𝑠𝑒𝑐𝑡𝑜𝑟
28𝑏. 𝑁𝑜𝑛𝑒, 𝑖𝑡 𝑖𝑠 𝑎
𝑚𝑖𝑑𝑠𝑒𝑔𝑚𝑒𝑛𝑡
28𝑐. 𝐴𝑙𝑡𝑖𝑡𝑢𝑑𝑒 − 𝐴𝐵 𝑖𝑠
𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑎
𝑠𝑖𝑑𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑣𝑒𝑟𝑡𝑒𝑥.
Inequalities in Triangles
Chapter 5 Section 3
Comparison Property of Inequality
If a = b + c, and c > 0, then a > b
A
B
C
If a = b + c, and c > 0, then a > b
Corollary to the Triangle Exterior Angle Theorem: The measure of an
exterior angle of a triangle is greater than the measure of each of its remote
interior angles
2
3
1
How would you write this mathematically?
m1  m2
m1  m3
PRACTICE: Explain why measure of angle 1 is greater than the measure of
angle 2.
2
3
4
1
2
3
4
1
Solution: 2 and 3 are congruent because they are alternate interior angles
between two parallel lines. Angle 1 is greater than angle 3, because an
exterior angle is larger than either of its interior angles. Since Angle 1 is
larger than angle 3, it is also larger than angle 2.
1. How many degrees are in the triangle?
2. Make a guess as to the measurement of each angle.
3. Which side is the smallest?
Y
Z
X
Theorem: If two sides of a triangle are not congruent,
then the larger angle lies opposite the longer side.
If XZ  XY , then mY  mZ
PRACTICE: List the angles of the triangle in order from smallest to largest
S
5
R
12
Q
PRACTICE: List the angles of the triangle in order from smallest to largest
Q  S  R
S
5
R
12
Q
A
B
C
Theorem: If two angles of a triangle are not congruent,
then the longer side lies opposite the larger angle.
if mA  mB, then BC  AC
Y
80 
58
X
Z
List the sides of the triangle in order from shortest to longest
Y
80 
58
X
42
Z
List the sides of the triangle in order from shortest to longest
XY  YZ  XZ
To create a triangle, what do you need?
Without altering the strips of paper
handed to you, create a triangle.
Theorem – The sum of the length of any two sides of a
triangle is greater than the length of the third side.
Y
XY  YZ  XZ
YZ  ZX  YX
ZX  XY  ZY
X
Z
The lengths of two sides of a triangle are given. Describe the possible
lengths for the third side:
7, 12
12
7
The side must be less than 19.
7
12
The side must be greater than 5.
5 < x < 18
Can a triangle have sides of the following measures?
1,2,3
No, 1+2 is not greater than 3
3,4,5
Yes, any two numbers are greater than the third number.
2,4,6
No, 2+4 is not greater than 6
8,10,12
Yes, any two numbers are greater than the third number.
30, 60, 90
No, 30 + 60 is not greater than 90.
1, 8, 10
No, 1 + 8 is not greater than 10.
The lengths of two sides of a triangle are given. Describe the possible
lengths for the third side:
3, 8
The side must be greater than 5, and less than 11.
x > 8-3, x > 5
x < 8+3, x < 11
9, 9
5 < x < 11
The side must be greater than 0, and less than 18.
x > 9-9, x>0
x < 9 + 9, x < 18
0 < x < 18
HOMEWORK: Complete the worksheet handed out in class today.
Upcoming Schedule
Next class: Review
Following Class: Test Chapter 5.1, 5.2, 5.3, 5.5, Midpoint and Distance
of a segment, graphing.