congruent figures
Can congruent shapes have different names?
Yes, congruent shapes can have different names, even if they are the same shape and size.
What are similar figures
Figures that have the same shape but a different size; the angles are congruent and the sides are proportionsal
What does SSS mean
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent
Surface Area Is:
The total area of the surface of a solid figure.
the sum of the area of all of its faces.
expressed in square units.
found by using a net.
What is the probability that 6 side dice will land on 3
1/6 .1666 16%
Rectangle ABCD is congruent to rectangle URST.
Rectangles A B C D and U R S T are congruent. The length of sides A B is 9 millimeters and the length of sides R S is 15 millimeters.
What is the area of rectangle URST?
135 mm²
what is a ratio
a comparsion of two numbers
In a right triangle, the adjacent side is 6 units, and the angle is 45°. What is the length of the hypotenuse?
8.49 units
A shape that has two dimensions, usually described in terms of length and breadth, or length and height.
Two-dimensional figures
A point is chosen at random inside a square with side length 10 cm. Inside the square, there is a circle of radius 5 cm perfectly inscribed (touching all four sides of the square). What is the probability that the randomly chosen point lies inside the circle?
78.5% 0.785
Are two triangles congruent if their corresponding sides and angles are the same?
Yes, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure.
What does it mean for two figures to be similar?
Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.
In a right triangle, if angle A is 40 degrees, and the adjacent side is 12 units long, what is the length of the hypotenuse?
15.67 units
What is the surface area of a cube with a side length of 5 cm?
150cm2
What is the probability of drawing a red card from a standard deck of cards?
A standard deck has 52 cards, and half of them are red (26 red cards). So the probability is 26/52 or 1/2
How can you prove two triangles are congruent using ASA (angle-side-angle) postulate
Two triangles are congruent by ASA if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
If two similar triangles have a side ratio of 3:5, what is the ratio of their areas?
The ratio of their areas is the square of the side ratio: (3/5)^2=9/25
what is sin 30°
1/2
What is the total surface area of a cylinder with a radius of 3 cm and height of 10 cm?
245.04 cm2
A bag contains 4 red, 5 blue, and 6 green marbles. What is the probability of randomly picking a red marble and then a blue marble without replacement?
20/210=2/21
A triangle has sides of 7 cm, 24 cm, and 25 cm. A second triangle has two sides measuring 7 cm and 24 cm, and the included angle is 90°. Are the two triangles congruent? Justify based on triangle congruence criteria.
Yes, they are congruent. Since both triangles have the same side lengths they are congruent by sss
Two rectangles are similar. The larger has dimensions 15 cm by 25 cm. The smaller has a perimeter of 32 cm. What is the area of the smaller rectangle?
Area = 60 cm²
In triangle ABC, angle C is 90°, and angle A is 30°. If side AC = 10 units, what is the length of side AB?
In a 30°-60°-90° triangle, the hypotenuse is twice the side opposite 30°. AC is adjacent to angle B (opposite angle A). So if angle A = 30°, side opposite (BC) is 10, and AB (hypotenuse) is 20.
A cylinder and a cone have the same height and the same radius. If the volume of the cylinder is 300π cm³, what is the total surface area of the cone?
Volume of cylinder = πr²h = 300π → r²h = 300
Let’s solve for r and h using assumed values: try r = 5 → h = 12 (since 25 × 12 = 300)
Now surface area of cone = πr² + πrℓ
ℓ = √(r² + h²) = √(25 + 144) = √169 = 13
→ Surface area = π(25) + π(5)(13) = 25π + 65π = 90π cm²
A bag contains 6 red, 5 blue, and 4 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are the same color?
Total marbles = 15
Ways to choose 2 of same color:
Red: C(6,2) = 15, Blue: C(5,2) = 10, Green: C(4,2) = 6 → total favorable = 31
Total ways to choose 2 = C(15,2) = 105
→ Probability = 31/105 = ~0.295