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Geometry Mini Quiz 12/10/15
1)
3) Fill in the chart. Write the name of the point of concurrency (where they meet).
2)
Altitudes Angle Bisector
Medians Perpendicular Bisector
WRITE DOWN!Use ½ sheet of paper1) ASSUME There are not at least 7 dogs OR There are 7 or more dogs
2) Assume N is not odd OR N is even
OrthocenterIncenter Centroid Circumcenter
5-5 Review Format for Indirect Proof• Step 1
• Assume temporarily that ________________________________.
• Step 2• _____________________________________________________
• Step 3• Then this contradicts the given statement that _________.
• Step 4• The temporary assumption that ____________ must be false.
• Step 5• So we can conclude that_____________________.
Ex. 1)• Step 1
• Assume temporarily that ________________________________.
• Step 2
• Step 3• Then this contradicts the given statement that _________.
• Step 4• The temporary assumption that ____________ must be false.
• Step 5• So we can conclude that_____________________.
X = 4
32 + 8y = 48
Plug in x = 4 into 8(x + y) = 48 8(4 + y) = 48
- 32 -328y = 16
y = 2
X = 4
5-6 INEQUALITIES IN ONE TRIANGLE
WRITE DOWN!
Triangle Inequality Theorem
A
C
B
Smallest Side Opposite
Smallest Angle
3
5
7
Side AB
C
Watch!
Triangle Inequality Theorem
A
B
C
Biggest Side Opposite
Biggest Angle
3
5
7
Side AC
B
Watch!
Ex 2) Triangle Inequality Theorem
Smallest Side =Smallest Angle =
Medium Side = Medium Angle =
Biggest Side =Biggest Angle =
Make a note: Biggest Side Opposite Biggest Angle
A
B
C
3
5
7
AC
B
CB
A
AB
C
LOOK AT Opposite Side & Angle
Ex 3) 60
ANGLES:
Small = 58 = U
Medium = 60 = T
Large = 62 = V
SIDES:
Small = opposite of U = TV
Medium = opposite of T = UV
Large = opposite of V = UT
Find the measure of angle T
Ex 4: List the measures of the sides of the triangle, in order of least to greatest.
10x - 10 = 180
Solving for x:B
A
C
Therefore, AB < AC < BC
least greatest
2x + 1
4x
4x -112x +1 + 4x + 4x - 11 =180
10x = 190
X = 19
A = 76o; B = 65o; C = 39o
A = 4(19) = 76o
B = 4(19) – 11 = 65o
C = 2(19) + 1 = 39o
Smallest = Angle CMedium = Angle BLargest = Angle A
Smallest = Side ABMedium = Side ACLargest = Side BC
Plug back in to angles:
Triangle Inequality TheoremThe sum of the 2 SMALLEST sides must be greater than the 3rd side.
Ex 5) Determine if the following lengths are legs of triangles
a) Good Example b) Bad Example
Small sides: 3 + 3 = 63rd side: 5
3+3> 5 YES! Sum of small sides is greater than 3rd side.
Yes, it is a triangle.
Small sides: 2 + 2 = 43rd side: 5
2+2>5 NO! Sum of small sides is NOT greater than 3rd side
No, it is not a triangle.
Ex 6) Determine if the following lengths are sides of triangles
a) 4, 9, 5
4 + 5 ? 9
9 > 9
We choose the smallest two of the three sides and add them together. Comparing the sum to the third side:
b) 9, 5, 5
Since the sum is not greater than the third side, this is not a
triangle
5 + 5 ? 9
10 > 9Since the sum is greater than the third side, this is
a triangle
Ex 7)
YES!No!
Ex 8)
Angles:
S = 24 smallest O = 130 largestX = 26 medium
Sides (opposite from angle):
OX = smallest XS = largestOS = medium
Shortest side = OXbecause angle S (opposite from side) is smallest.
Find measure of angle X
Ex 9) • Two sides of a triangle are 5 ft and 8 ft long. What is the
range of possible lengths for the third side?
Do ALL Combinations. Add 2 sides.
Must be greater than 3rd side.
Review