Basic Angles

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Transcript Basic Angles

Bellringer Use the diagram to identify 1 pair of each of the following: -Corresponding angles -Adjacent angles -Vertical angles

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Basic Angles Angle Relationships Triangles Congruent Triangles Pythagorean Theorem Volume

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Replay

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Go to Final Jeopardy

Basic Angles

$100 Angles a and b are congruent because of _______________ angles

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Basic Angles

$100 Angles a and b are congruent because of

Vertical

angles

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Basic Angles

$200 Which angle is adjacent to ∠ DGC?

a) ∠ b) ∠ c) ∠ d) ∠ FGA DGE EGF AGB

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Basic Angles

$200 Which angle is adjacent to ∠ DGC?

a) ∠ b) ∠ c) ∠ d) ∠ FGA DGE EGF AGB

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Basic Angles

$300 Write and solve an equation to find the measure of angle b.

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Basic Angles

$300 Write and solve an equation to find the measure of angle b. b + 63 = 90 -63 -63

b = 27˚

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Basic Angles

$400 Line l and m are parallel. Angle 8 is congruent to angle 2 because of_____________ ___________ _____________

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Basic Angles

$400 Line l and m are parallel. Angle 8 is congruent to angle 2 because of

Alternate Interior Angles

54

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Basic Angles

$500 If line p and line t are parallel, name one pair of corresponding angles.

Line p Line t

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Basic Angles

$500 If line p and line t are parallel, name one pair of corresponding angles.

A and E B and F C and G D and H

Line p Line p Line t Line t

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Angle Relationships

$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 ∠ x and ∠ y are complementary. ∠ x = (2w + 8)˚ and ∠ y = 14 ˚ What is the measure of ∠ x? ∠ x = (2w + 8)˚ (2w + 8) + 14 = 90 2w + 22 = 90 -22 -22 2w = 68 w = 34 ∠ x = 2(34) + 8 ∠ x = 68+ 8 ∠ x = 76˚

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Angle Relationships

$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 ∠ h and ∠ j are supplementary. ∠ h = 123˚ and ∠ j = (12+3x)˚ What is the measure of ∠ j? ∠ j = (12 + 3x)˚ (12 + 3x) + 123 = 180 3x + 135 = 180 -135 -135 3x = 45 x = 15 ∠ j = 12+ 3(15) ∠ j = 12+ 45 ∠ j = 57˚

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Angle Relationships

$300 Lines l and m are parallel. Angle 6 is supplementary to which angles?

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Angle Relationships

$300 Lines l and m are parallel. Angle 6 is supplementary to which angles? ∠ 2 ∠ 5 ∠ 1 ∠ 8

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Angle Relationships

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Angle Relationships

Which angles are adjacent?

a) ∠ HIK and ∠ JIF b) ∠ c) ∠ d) ∠ HIK and HIK and HIK and ∠ ∠ ∠ KIJ EFI DFG $400

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Angle Relationships

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Angle Relationships

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Triangles

$100 What is the missing angle measure?

x˚ 49˚ 56˚

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Triangles

$100 What is the missing angle measure?

56 + 49 + X = 180 105 + X = 180

X = 75

49˚ 56˚

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Triangles

$200 What is the missing angle measure?

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Triangles

$200 What is the missing angle measure?

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Triangles

$300 What is the missing angle measure?

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Triangles

$300 45 101 101 56 124 56

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Triangles

$400 Find the measure of angle M.

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Triangles

$400 x+5 + 2x-2 + 90 = 180 3x + 93 = 180 3x = 87

x = 29 So Angle M is 2(29) – 2 or 56 degrees

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Triangles

$500 What is the missing angle measure?

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Triangles

$500 64 116 116 64 66 50 50 130 130 50 66 50 64 116 130 116

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Congruent Triangles

$100 Which rule proves that these triangles are congruent?

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Congruent Triangles

$100 Which rule proves that these triangles are congruent?

side-angle-side

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Congruent Triangles

$200 Which rule proves that these triangles are congruent?

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Congruent Triangles

$200 Which rule proves that these triangles are congruent?

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side-side-side

Congruent Triangles

Which rule proves that these triangles are congruent?

$300 A.) angle-side-angle B.) side-side-angle C.) side-angle-side D.) none of the above

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Congruent Triangles

Which rule proves that these triangles are congruent?

$300 A.) angle-side-angle B.) side-side-angle C.) side-angle-side D.) none of the above -6

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Congruent Triangles

Which rule proves that these triangles are congruent?

$400 A.) angle-side-angle -10 – (-4) – 3 C.) side-angle-side D.) none of the above

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Congruent Triangles

Which rule proves that these triangles are congruent?

$400 A.) angle-side-angle B.) side-side-angle C.) side-angle-side D.) none of the above -9

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Congruent Triangles

Which rule proves that these triangles are congruent?

a = -9, b = 8, c = 1 B.) side-side-angle b – a – c D.) none of the above $500

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Congruent Triangles

Which rule proves that these triangles are congruent?

$500 A.) angle-side-angle B.) side-side-angle C.) side-angle-side D.) none of the above 16

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Pythagorean Theorem

$100 A triangle has sides with lengths of 6 inches, 9 inches and 14 inches. Is it a right triangle?

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Pythagorean Theorem

$100 A triangle has sides with lengths of 6 inches, 9 inches and 14 inches. Is it a right triangle?

No! the Pythagorean Theorem doesn’t work.

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Pythagorean Theorem

$200 What is the length of the missing side?

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Pythagorean Theorem

$200 What is the length of the missing side?

40 ft

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Pythagorean Theorem

$300 Find the distance between the two points shown. Round to the nearest tenth.

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Pythagorean Theorem

$300 Find the distance between the two points shown. Round to the nearest tenth.

4.2 units

3 3

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Pythagorean Theorem

$400 What is the length of the missing side?

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Pythagorean Theorem

$400 What is the length of the missing side?

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Pythagorean Theorem

$500 Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

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Pythagorean Theorem

$500 Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

9.4 miles

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Volume

$100 Find the volume of this figure. Round to the nearest tenth.

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Volume

Cylinder: $100 V = 3.14 x 5 2 x 7

549.5 yd 3

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Volume

$200 Find the volume of this figure. Round to the nearest tenth.

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Volume

CONE: $200 V = (1/3) x 3.14 x 4 2 x 7

117.2 m 3

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Volume

$300 Find the volume of this figure. Round to the nearest tenth.

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Volume

CYLINDER: V = 3.14 x 8 2 x 4 $300

803.8 m 3

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Volume

$400 The soccer ball is 22 cm across in diameter. Find its volume to the nearest tenth.

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Volume

$400 SPHERE: (radius is 11 cm) V = (4/3) x 3.14 x 11

3 5572.5 cm 3

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Volume

$500 A cone has a height of 3.2 inches and a volume of 53.59 cubic inches. Find the radius.

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Volume

Cone: $500 V = (1/3) x 3.14 x r 2 x h 53.59 = (1/3) x 3.14 x r 2 x 3.2

53.59 = 3.35 x r 2 16 = r 2 …so r = 4 inches

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D aily D o u b l e

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J e F inal d y

Today’s Category: Pythagorean Theorem

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In Mike’s basketball game he ran 9 feet straight out from under the basket. Then he went left 4 feet before running straight back to his original spot under the basket. How far did Mike travel? Round to the nearest tenth.

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4 ft 9 ft 9.8 ft Mike traveled a total of 22.8 feet.

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Remember to study for the test!