BellringerBellringerUse the diagram to identify 1 pair of each of the following:

-Corresponding angles-Adjacent angles-Vertical angles

GeometryGeometryGeometryGeometryJEOPARDYJEOPARDYJEOPARDYJEOPARDY

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PPLLAAYY

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PPLLAAYY

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Basic Angles

Congruent Triangles

Pythagorean Theorem

VolumeTriangles

Go to Final JeopardyReplay

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Angle Relationships

GEO

METR

Y JEO

PA

RD

YG

EO

METR

Y JEO

PA

RD

YG

EO

METR

Y JEO

PA

RD

YG

EO

METR

Y JEO

PA

RD

Y

Angles a and b are Angles a and b are congruent because of congruent because of

_______________ angles_______________ angles

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Basic Angles $100$100

Angles a and b are Angles a and b are congruent because of congruent because of

VerticalVertical anglesangles

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Basic Angles $100$100

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Basic Angles $200$200

Which angle is adjacent to DGC?∠

a) FGA∠b) DGE∠c) EGF∠d) AGB∠

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Basic Angles $200$200

Which angle is adjacent to DGC?∠

a) FGA∠b) DGE∠c) EGF∠d) AGB∠

Write and solve an Write and solve an equation to find the equation to find the

measure of angle b. measure of angle b.

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Basic Angles $300$300

Write and solve an equation to Write and solve an equation to find the measure of angle b. find the measure of angle b.

b + 63 = 90b + 63 = 90

-63 -63 -63 -63

b = 27˚b = 27˚

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Basic Angles $300$300

Line l and m are parallel. Angle 8 Line l and m are parallel. Angle 8 is congruent to angle 2 because is congruent to angle 2 because of_____________ ___________ of_____________ ___________

_____________ _____________

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Basic Angles $400$400

5454

Line l and m are parallel. Angle 8 Line l and m are parallel. Angle 8 is congruent to angle 2 because is congruent to angle 2 because

of of Alternate Interior AnglesAlternate Interior Angles

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Basic Angles $400$400

If line p and line t are parallel, If line p and line t are parallel, name one pair of name one pair of corresponding angles.corresponding angles.

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Basic Angles $500$500

Line p

Line t

If line p and line t are parallel, If line p and line t are parallel, name one pair of corresponding name one pair of corresponding angles.angles.

A and EA and E

B and FB and F

C and GC and G

D and HD and H

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Basic Angles $500$500

Line p

Line t

Line p

Line t

∠x and y are complementary. ∠

∠x = (2w + 8)˚ and y = 14 ∠˚ What is the measure of

x? ∠

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Angle Relationships $100$100

∠x and y are complementary. ∠

∠x = (2w + 8)˚ and y = 14 ˚ ∠What is the measure of x? ∠

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Angle Relationships $100$100

∠x = (2w + 8)˚

∠x = 2(34) + 8

∠x = 68+ 8∠x = 76˚

(2w + 8) + 14 = 902w + 22 = 90 -22 -222w = 68w = 34

∠h and j are supplementary. ∠

∠h = 123˚ and j = (12+3x)˚ ∠What is the measure of j? ∠

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Angle Relationships $200$200

∠h and j are supplementary. ∠

∠h = 123˚ and j = (12+3x)˚ ∠What is the measure of j? ∠

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Angle Relationships $200$200

∠j = (12 + 3x)˚

∠j = 12+ 3(15)

∠j = 12+ 45∠j = 57˚

(12 + 3x) + 123 = 1803x + 135 = 180 -135 -1353x = 45x = 15

Lines l and m are parallel. Angle Lines l and m are parallel. Angle 6 is supplementary to which 6 is supplementary to which

angles? angles?

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Angle Relationships $300$300

Lines l and m are parallel. Angle Lines l and m are parallel. Angle 6 is supplementary to which 6 is supplementary to which

angles? angles?

∠ 22

∠ 55

∠ 11

∠ 88$300

Angle Relationships $300$300

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Angle Relationships $400$400

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Angle Relationships $400$400Which angles are adjacent?a) HIK and JIF∠ ∠b) HIK and KIJ∠ ∠c) HIK and EFI∠ ∠d) HIK and DFG∠ ∠

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Angle Relationships $500$500

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Angle Relationships $500$500

What is the missing What is the missing angle measure?angle measure?

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Triangles $100$100

x˚

56˚49˚

What is the missing What is the missing angle measure?angle measure?

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Triangles $100$100

x˚

56˚49˚

75˚

56 + 49 + X = 180

105 + X = 180

X = 75

What is the missing What is the missing angle measure?angle measure?

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Triangles $200$200

What is the missing What is the missing angle measure?angle measure?

$200$200

Triangles $200$200

What is the missing What is the missing angle measure?angle measure?

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Triangles $300$300

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Triangles $300$300

101101

45

5656

124

Find the measure of Find the measure of angle M.angle M.

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Triangles $400$400

$$400

Triangles $400$400

x+5 + 2x-2 + 90 = 180

3x + 93 = 180

3x = 87

x = 29

So Angle M is 2(29) – 2 or 56 degrees

What is the missing angle What is the missing angle measure?measure?

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Triangles $500$500

$$500

Triangles $500$500

50

50 130

50

50

130

130

64 116

116

116

11664

64

66

66

Which rule proves that Which rule proves that these triangles are these triangles are

congruent?congruent?

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Congruent Triangles $100$100

Which rule proves that Which rule proves that these triangles are these triangles are

congruent?congruent?

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Congruent Triangles $100$100

side-angle-side

Which rule proves that Which rule proves that these triangles are these triangles are

congruent?congruent?

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Congruent Triangles $200$200

Which rule proves that Which rule proves that these triangles are these triangles are

congruent?congruent?

$200$200

Congruent Triangles $200$200

side-side-side

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Congruent Triangles $300$300Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

-6-6

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Congruent Triangles $300$300Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

-10 – (-4) – 3 -10 – (-4) – 3

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Congruent Triangles $400$400Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

-9-9

$400$400

Congruent Triangles $400$400Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

a = -9, b = 8, c = 1a = -9, b = 8, c = 1

b – a – cb – a – c

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Congruent Triangles $500$500Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

1616

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Congruent Triangles $500$500Which rule proves that these triangles are congruent?

A.) angle-side-angleB.) side-side-angle C.) side-angle-sideD.) none of the above

A triangle has sides with A triangle has sides with lengths of 6 inches, 9 lengths of 6 inches, 9

inches and 14 inches. Is inches and 14 inches. Is it a right triangle?it a right triangle?

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Pythagorean Theorem $100$100

A triangle has sides with A triangle has sides with lengths of 6 inches, 9 lengths of 6 inches, 9

inches and 14 inches. Is inches and 14 inches. Is it a right triangle?it a right triangle?

No! the Pythagorean No! the Pythagorean Theorem doesn’t work. Theorem doesn’t work.

$100$100

Pythagorean Theorem $100$100

What is the length of the What is the length of the missing side?missing side?

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Pythagorean Theorem $200$200

What is the length of the What is the length of the missing side?missing side?

$300$300

Pythagorean Theorem $200$200

40 ft

Find the distance between Find the distance between the two points shown. the two points shown. Round to the nearest tenth.Round to the nearest tenth.

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Pythagorean Theorem $300$300

Find the distance between Find the distance between the two points shown. the two points shown. Round to the nearest tenth.Round to the nearest tenth.

4.2 units4.2 units

$100$100

Pythagorean Theorem $300$300

3

3

What is the length of the What is the length of the missing side?missing side?

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Pythagorean Theorem $400$400

What is the length of the What is the length of the missing side?missing side?

$400$400

Pythagorean Theorem $400$400

15 cm

Two joggers run 8 miles north Two joggers run 8 miles north and then 5 miles west. What is and then 5 miles west. What is

the shortest distance, to the the shortest distance, to the nearest tenth nearest tenth of a mile, they of a mile, they must travel to return to their must travel to return to their

starting point?starting point?

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Pythagorean Theorem $500$500

Two joggers run 8 miles north Two joggers run 8 miles north and then 5 miles west. What and then 5 miles west. What

is the shortest distance, to the is the shortest distance, to the nearest tenth nearest tenth of a mile, they of a mile, they must travel to return to their must travel to return to their

starting point?starting point?

9.4 miles9.4 miles

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Pythagorean Theorem $500$500

Find the volume of this figure. Find the volume of this figure. Round to the nearest tenth.Round to the nearest tenth.

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Volume $100 $100

Cylinder:Cylinder:

V = 3.14 x 5V = 3.14 x 522 x 7x 7

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Volume $100$100

549.5 yd3

Find the volume of this figure. Find the volume of this figure. Round to the nearest tenth.Round to the nearest tenth.

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Volume $200$200

CONE:CONE:

V = (1/3) x 3.14 x 4V = (1/3) x 3.14 x 422 x 7 x 7

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Volume $200$200

117.2 m3

Find the volume of this figure. Find the volume of this figure. Round to the nearest tenth.Round to the nearest tenth.

nextnext

Volume $300$300

CYLINDER:CYLINDER:

V = 3.14 x 8V = 3.14 x 822 x 4 x 4

803.8 m803.8 m33

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Volume $300$300

The soccer ball is 22 cm across The soccer ball is 22 cm across in diameter. Find its volume to in diameter. Find its volume to the nearest tenth.the nearest tenth.

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Volume $400$400

SPHERE: (radius is 11 cm)SPHERE: (radius is 11 cm)

V = (4/3) x 3.14 x V = (4/3) x 3.14 x 111133

5572.5 cm5572.5 cm3 3

$400$400

Volume $400$400

A cone has a height of 3.2 A cone has a height of 3.2 inches and a volume of inches and a volume of 53.59 cubic inches. 53.59 cubic inches.

Find the radius.Find the radius.

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Volume $500$500

Cone:Cone:

V = (1/3) x 3.14 x rV = (1/3) x 3.14 x r22 x h x h

53.59 = (1/3) x 3.14 x r53.59 = (1/3) x 3.14 x r22 x 3.2 x 3.2

53.59 = 3.35 x r53.59 = 3.35 x r22

16 = r16 = r22 … …so r = 4 inchesso r = 4 inches

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Volume $500$500

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Today’s Category:Pythagorean Theorem

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In Mike’s basketball game he In Mike’s basketball game he ran 9 feet straight out from ran 9 feet straight out from under the basket. Then he under the basket. Then he

went left 4 feet before running went left 4 feet before running straight back to his original straight back to his original

spot under the basket. How far spot under the basket. How far did Mike travel? Round to the did Mike travel? Round to the

nearest tenth.nearest tenth.nextnext

Mike traveled a total of Mike traveled a total of 22.8 feet.22.8 feet.

nextnext

9 ft

4 ft

9.8 ft

GeometryGeometryGeometryGeometryJEOPARDYJEOPARDYJEOPARDYJEOPARDY

Thanks forThanks forPPLLAAYYIINNGG!!Thanks forThanks forPPLLAAYYIINNGG!!

Remember to study for the test!