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