Congruent figures
Are two triangles with the same shape and size always congruent?
Yes they are!
What are the 3 similarities?
AA, SSS, SAS
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10, what is the length of the side opposite the 30 degree angle?
5
A cube has sides of 3cm. What is the surface area?
54cm2
A bag contains 5 red marbles and 3 blue marbles. If you randomly pick two marbles from the bag without looking, what is the probability that you pick one red marble and one blue marble? Express your answer as a simplified fraction.
15/28
What does it mean for two figures to be congruent?
They have same size and shape , never change.
What does it mean for two figures to be similar?
Two figures are similar if they are the same shape but can be different sizes.
In a right triangle, the side opposite angle C is 3 units, and the side adjacent to angle C is 4 units. Find the tangent of angle C.
tan(C) = 3/4= 0.75
A rectangurlar prism is 6 cm long, 2 cm wide and 4 cm high.Calcuate its volume.
48cm3
You roll a standard six-sided die. What is the probability of rolling an even number? Express your answer as a simplified fraction.
1/2
Two triangles, △ABC and △DEF, are congruent. If AB = 5 cm, BC = 7 cm, and ∠B = 60°, what are the corresponding side and angle measures in triangle DEF?
DE = 5 cm, EF = 7 cm, and ∠E = 60°
If triangle ABC is similar to triangle XYZ, and AB=5, XY=10, and BC=7, what is the length of YZ?
14
In a right-angled triangle, one of the acute angles is 45 degrees, and one of the legs (the sides that form the right angle) has a length of 7 units. What is the length of the other leg?
7
A cylinder has a radius of 5cm and a hieght of 10 cm. what is its total surfaces area?
471.24cm2
Imagine you have a spinner divided into four equal sections colored red, blue, green, and yellow. If you spin the spinner once, what is the probability that it will land on either the color blue or the color yellow? Express your answer as a simplified fraction.
1/2
If two triangles are congruent by the Side-Angle-Side?
Two pairs of corresponding sides and the included angle between them must be equal.
Two similar pentagons have a side length ratio of 3:5. If the perimeter of the smaller pentagon is 45, what if the perimeter of the larger pentagon?
75
In a right-angled triangle, one of the acute angles measures 30 degrees, and the side opposite this angle has a length of 5 units. What is the length of the hypotenuse of this triangle?
10
a square pyramid has a base with sides of 4cm and a slant height of 6cm. find its total surfaces area.
64cm2
You have a jar containing 10 marbles: 6 are green and 4 are orange. If you randomly pick one marble from the jar, what is the probability that the marble you pick is green? Express your answer as a simplified fraction.
3/5
triangles ABC and DEF, AB = DE, BC = EF, and ∠B = ∠E. Can you conclude that the two triangles are congruent?
Yes, the two triangles are congruent by the SAS
A square pyramid has a base side length of 6 and a height of 8. A similar pyramid has a base side length of 9. What is the height of the similar pyramid, and by what factor does the volume increase?
The height of the similar pyramid is 12, and the volume increases by a factor of 27/8
In triangle XYZ,angle X is 45 degrees, angle Y is 45 degrees, and side x (opposite angle X) is 12 units. What is the length of side y (opposite angle Y?
Y=12 units
A sphere has a volume of 500cm3. whats the sufaces area.
248,94cm2
You flip a fair coin twice. What is the probability of getting heads on the first flip and tails on the second flip? Express your answer as a simplified fraction.
1/4