Congruent figures
Can congruent figures be different colors?
Yes! Congruent figures can be different colors as long as they have the same size and shape. Color doesn't affect congruence; only size and shape matter.
What does it mean for two shapes to be similar?
Two shapes are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional.
What is the sine of a 30° angle in a right triangle?
In a right triangle, the sine of a 30° angle is 0.5. This means the length of the side opposite the 30° angle is half the length of the hypotenuse.
What is the surface area of a cube with a side length of 4 cm?
The surface area (SA) of a cube is calculated using the formula:
SA = 6 × side²
SA = 6 × (4 cm)² = 6 × 16 cm² = 96 cm²
A coin is flipped once. What is the probability of getting tails?
Number of favorable outcomes / Total outcomes = 1 / 2 = 0.5 or 50%
Possible outcomes: Heads or Tails
What does it mean for two shapes to be congruent?
Two shapes are congruent if they have the same size and shape. This means all their sides and angles are equal, and one can be transformed into the other through flipping, rotating, or sliding without changing its dimensions.
Are all squares similar?
Yes, all squares are similar because they have the same shape and equal angles, even though their sizes may differ.
How do you calculate the cosine of a 45° angle?
For a 45° angle in a right triangle, the cosine is approximately 0.707. This value is derived from the ratio of the adjacent side to the hypotenuse.
What is the volume of a sphere with a radius of 3 cm?
The volume (V) of a sphere is given by the formula:
V = (4/3) × π × radius³
V = (4/3) × π × (3 cm)³ = (4/3) × π × 27 cm³ ≈ 113.1 cm³
If a fair six-sided die is rolled, what is the probability of rolling a number greater than 4?
Possible outcomes: 1, 2, 3, 4, 5, 6
Probability = Number of favorable outcomes / Total outcomes = 2 / 6 = 1/3 ≈ 0.3333 or 33.33%
Are these two triangles congruent?
Yes, if two triangles have corresponding sides of equal length and corresponding angles of equal measure, they are congruent. For example, if triangle ABC has sides AB = 5 cm, BC = 6 cm, and AC = 7 cm, and another triangle DEF has sides DE = 5 cm, EF = 6 cm, and DF = 7 cm, then triangle ABC ≅ triangle DEF.
If two triangles are similar, what can we say about their corresponding sides?
If two triangles are similar, their corresponding sides are proportional. This means the ratio of the lengths of corresponding sides is constant.
What is the tangent of a 60° angle?
The tangent of a 60° angle is approximately 1.732. This ratio compares the length of the opposite side to the adjacent side in a right triangle.
What is the volume of a cylinder with a radius of 4 cm and a height of 10 cm?
The volume (V) of a cylinder is calculated using the formula:
V = π × radius² × height
V = π × (4 cm)² × 10 cm = π × 16 cm² × 10 cm = 160π cm³ ≈ 502.65 cm³
What is the probability of drawing a red marble from a jar containing 3 red, 7 green, and 10 white marbles?
Total marbles = 3 red + 7 green + 10 white = 20 marbles
Probability of drawing a red marble = Number of red marbles / Total marbles = 3 / 20 = 0.15 or 15%