Congruent Figures
If two shapes have the same size and shape are they congruent?
Yes
What are the three main triangle functions
Sine (Sin) Cosine (Cos) and Tangent (Tan)
Given two similar triangles how can you determine the scale factor between them?
Ranks of corresponding length simply divide the length of a side and the length
What is the Volume of a rectangular prism that is 10 feet wide, 8 feet tall, and 12 feet long
960 ft3
What are the symbols used for probability when you wish to have "and" values and "or" values
AnB and AuB
Two triangles are congruent if they have the same three side lengths. What is the congruence test called?
Side-Side-Side (SSS)
What is the longest side on a triangle called
Hypotenuse
If two figures are similar, what can you conclude about the ratio of their corresponding angles and sides?
Corresponding angles are congruent and have equal ratios of the lengths.
What is the area of a fence that is 10 feet long and 40 feet wide
400 ft2
What is the difference between dependent and independent events.
Independent events are not affected by other events (e.g. a coin landing on heads twice) and Dependent events rely on something else happening (e.g. drawing a club after drawing another card from a deck and leaving it out)
What is the hypotenuse of a right triangle with a base of 6 meters and a height of 10 meters
62 m + 102 m = 1362 = 11.66 m
Two Similar polygons have perimeters of 20 and 30 feet respectively. If one side of the smaller polygon has length of 4 units what is the length of the corresponding side of the larger polygon?
ratio=20/30
20=4*3
4/x=2/3
2x=12
x=12/2=6
6 ft
John is reusing old soda cans for an art project, he finds a soda can with a base diameter of 10 in and a height of 4 in. How Much Material does John have?
2π(5)(4)+2π(5)2 = 90 in2
What is the chance of 2 dice landing on 6
1/6 * 1/6 = 1/12
IN Parallelogram PQRS, diagonal PR is drawn. Prove that triangle PQR is congruent to triangle PSR
Use SSS. PQ=RS, PS=QR, and PR is shared
In a Right triangle, angle A=30o and the hypotenuse is 12 cm find the length of the side opposite angle A
Sin (30o) x/12 -> x= Sin (30o) * 12 = 6
A rectangle with sides of 4 cm and 6 cm respectively is similar to another rectangle with a side of 10 cm. what are the dimensions of the large rectangle
4/6 = 2/3
10/4 = 5/2
6*5/2 = 15 cm
Bill is painting a wooden plank that is 10 inches long, 4 inches wide and 12 inches tall. how much paint will he use?
2(10*4+10*12+4*12) = 416 in2
The football team has 2 Juniors 3 Sophomores and 6 seniors what are the chances one player on the team selected on random is a Junior.
2/11
In a trapezoid ABCD where AB is parallel to CD, AB=BC and angle A = angle B prove that ABCD is an isosceles trapezoid
Use ASA to prove trianles ADC and BDC are congruent so AD=BC and angle A = angle B
In Triangle ABC Angle A=40o Side A= 8 cm and Side = 10 cm
find Angle B.
Sin(40o)/8 = Sin B/10
Sin B (10*(Sin40o))/8
Sin B =
sinB=(10*0.642)/8=86.42/8=0.8035
B=sin−1(0.8035)≈53.3o
What is the difference between congruent and similar figures?
Similar figures have the same angle measures but have sides that are scaled by a common factor. Congruent means same side length and same angles
A triangular prism has a triangle with a base of 6 cm a height 10 cm. what is the volume of the prism?
V= 1/4*10*√(-6⁴⁺2*(6*6)² + 2*(6*6) - 6⁴+2*(6*6)² - 6⁴) = 155.88 cm²
In a group of 100 students:
60 study English
50 study History
35 study both English and History
20 study neither
What is the probability that a randomly selected student studies only one subject?
OE = 60 − 35 = 25
OH = 50 − 35 = 15
1S = 25 + 15 = 40
P(1S)=40/100 = 2/5