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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P L A Y
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N G !
Remember to study for the test!