Download 32-honors

LESSON PLAN
Kiea Brown
Geometry (5.6/5.7)
Objective: SWBAT use and apply inequalities involving angles and sides of triangles. Application of SAS inequality and SSS
inequality to form conclusions about two triangles. (day 32-HONORS)
Warm-Up: SOL and review questions/attendance/check hw
Presentation: “Triangle Inequalities”……….Storytime
Theorem: The ⊥ segment from a point to a line is the shortest segment. Draw a picture.
Activity: Protractor, Ruler, Notebook paper (Work together in pairs)
1. Draw a scalene triangle on a sheet of paper or on the dry erase board.
Label the triangle as ∆𝐶𝐴𝑇.
2. Each side of the triangle is measure in _________(what units) and each angle in ___________(what units).
Now name each side of the triangle: __________, __________, _________
Now name each angle of the triangle: _________, __________, _________
3. Draw a square around the measure of the longest side.
Draw a square around the angle that lies opposite the longest side.
Make a conjecture about the measures of the angles based upon the measure of the opposite sides.
4. Raise your hand when you have finished for your classgrade 
Theorem- In a  , if two angles are not congruent then larger side is opposite the larger angle.
(The converse is also true)
In a  , if two sides are not congruent then the larger angle is opposite the longer side.
(The converse is also true)
Ex: Name in descending order.
1.
2.
A
A
3.
A
50𝑜
𝑜
30
19
17
60𝑜
B
C
B
B
C
20
C
Theorem- in a , the lengths of any two sides must be larger than the third side to form a triangle.
Example-Can the
4. 7, 7 , 9
 be formed?
5. 6, 4, 2
Between what two values must the third side lie?
8. 8 and 9
9. 6 and 15
6. 11, 5, 8
7. 4, 10, 6
10. 12 and 7
11. 2.3 and 9.2
SAS inequality- if 2 sides of one
be greatest.
11.
 are 
D
12.
A
7
to 2 sides of another and the included angles are not
30𝑜
10
15
𝑜
80
80𝑜
B
11
E
12
14.
the side opposite the largest < will
N
P
50𝑜 53𝑜 12
50𝑜
F
Q
M
G
C
J
13.

L
R
K
X
10
27𝑜
15
Z
Y
85𝑜 7
SSS inequality- if 2 sides of one
the larger side is larger.

to 2 sides of another, but the third side of one
A
15.
C
11
G
E
10
12
N
SAS inequality  draw conclusions about sides
Class Exercises: use power point examples
Homework: worksheet
rd
4
Y
11
15
I
SSS inequality

side

the angle opposite
R
15
2
1
H
7
F
18
10
4
7
M
 is greater than the 3
17.
3
L
B
15
D
16.
12
10
H
11
I
draw conclusions about angles
I
3
K
12
SAS and SSS Inequality Practice Problems (CW day____)
1-7. Highlight those that form a triangle. If a triangle can be formed, list the angles in descending order. (Diagrams not drawn to scale)
E
13
D
P
T
12
14
F
13.5
W
17
3
S
U
14
10.5
R
∆𝐴𝐵𝐶: ̅̅̅̅
𝐴𝐵 = 𝑥, ̅̅̅̅
𝐴𝐶 = 𝑥 + 2, ̅̅̅̅
𝐵𝐶 = 𝑥 + 3
4
Q
V
6.5
∆𝑇𝑂𝑃: ̅̅̅̅
𝑇𝑂 = 4
̅̅̅̅
𝑃𝑂 = 12, ̅̅̅̅
𝑃𝑇 = 10
X
∆𝑆𝑈𝑁 ℎ𝑎𝑠 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 86. ̅̅̅̅
𝑆𝑈 = 2𝑥 + 8, ̅̅̅̅
𝑈𝑁 = 4𝑥, ̅̅̅̅
𝑆𝑁 = 3𝑥 + 6
8-16. Highlight those that form a triangle. If a triangle can be formed, list the sides in ascending order. (Diagrams not drawn to scale)
E
B
65𝑜
H
𝑜
36
I
K
K
75𝑜
75.5𝑜
70𝑜
A
C
F
D
D
J
I
L
∆𝐴𝐵𝐶: ∡𝐵 = 92𝑜 , ∡𝐴 = 41𝑜
10𝑜
M
M
L
H
J
∆𝑆𝑅𝑇: ∡𝑆 = 75𝑜 , 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 ∡𝑆𝑅𝑀 = 107𝑜
120𝑜
E
F
17. List the sides of ∆𝐴𝐵𝐶 in descending order, given: 𝑚∠𝐴 = (8𝑥 − 3)𝑜 , 𝑚∠𝐵 = (3𝑥 − 8)𝑜 𝑎𝑛𝑑 𝑚∠𝐶 = (74 − 2𝑥)𝑜
18. Given ∆𝐶𝐴𝑇 with ̅̅̅̅
𝐶𝐴 = 25 𝑐𝑚, ̅̅̅̅
𝑇𝐴 = 23 𝑐𝑚 𝑎𝑛𝑑 ̅̅̅̅
𝐶𝑇 = 24 𝑐𝑚. Highlight the true statement(s).
̅̅̅̅
̅̅̅̅
∠𝐴 < ∠𝑇 < ∠𝐶
∠𝐶 < ∠𝐴 < ∠𝑇
𝐶𝐴 > ̅̅̅̅
𝐴𝑇 > ̅̅̅̅
𝐶𝑇
𝐴𝑇 < ̅̅̅̅
𝐶𝑇 > ̅̅̅̅
𝐶𝐴
̅̅̅̅
̅̅̅̅
̅̅̅̅
∠𝐴 < ∠𝐶 < ∠𝑇
∠𝑇 > ∠𝐶 > ∠𝐴
𝑇𝐴 < 𝐶𝑇 < 𝐶𝐴
∆𝐶𝐴𝑇 𝑖𝑠 𝑎𝑛 𝑎𝑐𝑢𝑡𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
19-25. Determine which side measures will form a triangle. Underline those that form a right triangle. Highlight those that form a
obtuse triangle. Put a rectangle around those that form an acute triangle.
2, 3 and 4
9, 10 and 20
14, 17 and 31
3, 4 and 5
15, 17 and 19
(3, 5), (4, 7) and (7, 6)
(1, -5), (-3, 0) and (-1, 0)
26-27. For each of the problems below, highlight the possible values for the third side of the triangle(s)..
side lengths 5 and 9:
4, 7.8, 10, 12.9
side lengths 7 and 14:
5, 11, 15, 18, 22
28-29. For each of the problems below, highlight the values that will not form triangle(s).
side lengths 1 and 1:
0.5, 1.9, 2, 8
side lengths 18 and 22:
2, 4, 17, 25, 39, 40, 45
30. Find the two longest sides of ∆𝐴𝐵𝐶 𝑤𝑖𝑡ℎ 𝑚∡𝐶 = 67𝑜 and 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑚∡𝐵𝐴𝐺 = 108𝑜
31. Find the two shortest sides of ∆𝐴𝐵𝐶 𝑤𝑖𝑡ℎ 𝑚∡𝐵 = 67𝑜 and 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑚∡𝐵𝐶𝐾 = 114𝑜
32-34. Name the shortest length.
36-38. What can be concluded for each of the three pairs?
35. Using the diagram, which must be true?
𝐴𝑆 < 𝑌𝑈
𝑆𝐾 > 𝑌𝑈
𝑆𝐾 < 𝑌𝑈 𝐴𝐾 = 𝑂𝑈
Honors Geometry: Triangle Inequalities HW (day _____)
Name _____________ Block _____