#### 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**

**Basic Angles**

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

**Basic Angles **

$100 Angles a and b are congruent because of

*Vertical*

angles

**Basic Angles **

$200 Which angle is adjacent to ∠ DGC?

a) ∠ b) ∠ c) ∠ d) ∠ FGA DGE EGF AGB

**Basic Angles **

$200 Which angle is adjacent to ∠ DGC?

a) ∠ b) ∠ c) ∠ d) ∠ FGA DGE EGF AGB

**Basic Angles **

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

**Basic Angles **

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

## b = 27˚

**Basic Angles **

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

**Basic Angles **

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

*Alternate Interior Angles*

54

**Basic Angles **

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

Line p Line t

**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

**Angle Relationships**

$100 ∠ x and ∠ y are complementary. ∠ x = (2w + 8)˚ and ∠ y = 14 ˚ What is the measure of ∠ x?

**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˚

**Angle Relationships**

$200 ∠ h and ∠ j are supplementary. ∠ h = 123˚ and ∠ j = (12+3x)˚ What is the measure of ∠ j?

**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˚

**Angle Relationships**

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

**Angle Relationships **

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

**Angle Relationships**

$400

**Angle Relationships**

Which angles are adjacent?

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

**Angle Relationships**

$500

**Angle Relationships**

$500

**Triangles**

$100 What is the missing angle measure?

x˚ 49˚ 56˚

**Triangles**

$100 What is the missing angle measure?

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

**X = 75**

49˚ 56˚

**Triangles**

$200 What is the missing angle measure?

**Triangles**

$200 What is the missing angle measure?

**Triangles**

$300 What is the missing angle measure?

**Triangles**

$300 45 101 101 56 124 56

**Triangles**

$400 Find the measure of angle M.

**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**

**Triangles**

$500 What is the missing angle measure?

**Triangles**

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

**Congruent Triangles**

$100 Which rule proves that these triangles are congruent?

**Congruent Triangles**

$100 Which rule proves that these triangles are congruent?

side-angle-side

**Congruent Triangles**

$200 Which rule proves that these triangles are congruent?

**Congruent Triangles**

$200 Which rule proves that these triangles are congruent?

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

**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

**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

**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

**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

**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

**Pythagorean Theorem**

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

**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.

**Pythagorean Theorem**

$200 What is the length of the missing side?

**Pythagorean Theorem**

$200 What is the length of the missing side?

40 ft

**Pythagorean Theorem**

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

**Pythagorean Theorem**

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

4.2 units

**3 3**

**Pythagorean Theorem**

$400 What is the length of the missing side?

**Pythagorean Theorem**

$400 What is the length of the missing side?

**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?

**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

**Volume**

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

**Volume **

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

**549.5 yd 3**

**Volume **

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

**Volume **

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

**117.2 m 3**

**Volume **

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

**Volume **

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

**803.8 m 3**

**Volume **

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

**Volume **

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

**3 5572.5 cm 3 **

**Volume **

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

**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**

**Today’s Category: Pythagorean Theorem**

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.

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

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