Congruent Figures
1. What does it mean for two figures to be congruent?
Two figures are congruent if they have the same shape and size, but they may be rotated, reflected, or translated.
1. What does it mean for two figures to be similar?
Two figures are similar if they have the same shape but not necessarily the same size; their corresponding angles are equal, and their corresponding sides are in proportion.
1. What is the sine (sin) of an angle in a right triangle?
Sine of an angle = opposite side / hypotenuse.
1. What is the formula for the surface area of a rectangular prism?
Surface Area = 2(lw + lh +wh), where / = length, w = width, h = height.
1. A bag contains 3 red balls and 2 blue balls. What is the probability of randomly selecting a red ball?
Total balls = 3 + 2 = 5
Probability of red = 3/5
2. Are two triangles with the same side lengths and angle measures always congruent? Why or why not?
Yes, if two triangles have the same side lengths and angles measure, they are always congruent because they are identical in shape and size.
2. Are all congruent figures also similar? Why or why not?
Yes, all congruent figures are also similar because they have the same shape and size, which means their corresponding sides are in proportion and angles are equal.
2. What is the cosine (cos) of an angle in a right triangle?
Cosine of an angle = adjacent side / hypotenuse.
2. What is the formula for the volume of a cylinder?
Volume = π2h, where r = radius and h = height.
2. A fair coin is flipped once. What is the probability of getting heads?
There are 2 outcomes: head or tails.
Probability of heads = 1/2
3. Which triangle congruence shortcuts can be used to prove that two triangles are congruent?
The triangle congruence shortcuts are: SSS (Side-Side-Side), SAS (Side Angle Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).
3. How can you determine if two triangles are similar?
Two triangles are similar if they meet one of these criteria: AA (Angle-Angle), SSS (Side-Side-Side in proportion), or SAS (Side-Angle-Side with sides in proportion and the included angel equal).
3. What is the tangent (tan) of an angle in a right triangle?
Tangent of an angle = opposite side / adjacent side.
3. A cube has sides of length 4 cm. What is its surface area and volume?
Surface Area = 6 x (42) = 6 x 16 = 96 cm2
Volume = 43 = 64 cm3
3. A number is chosen at random from 1 to 10. What is the probability that is is an even number?
Even numbers between 1 and 10 = 2, 4, 6, 8, 10 → 5 numbers
Total outcomes = 10
Probability = 5/10 = 1/2
If two rectangles have the same side lengths, are they congruent?
Yes, rectangles with the same side lengths are congruent because all angles are 90 degrees and the side lengths match exactly.
4. If two similar rectangles have side lengths of 4 cm and 8 cm on one rectangle, and 6 cm and 12 cm on the other, are they similar?
Yes, they are similar because the sides are in the same ratio: 4:6 = 8:12 = 2:3.
4. In a right triangle, if one acute angle is 30 degrees and the hypotenuse is 10 units, what is the length of the side opposite the 30 degree angle?
Use: sin (30 degree) = opposite / hypotenuse
0.5 = opposite / 10
Opposite = 0.5 x 10 = 5 units
4. What is the surface area of sphere with a radius of 5 cm?
Surface Area = 4πr2 = 4π(25) = 100π~ 314.16 cm2
4. Two dice are rolled. What is the probability that the sum is 7?
There 6 x 6 = 36 possible outcomes.
Combinations that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 combinations
Probability = 6/36 = 1/6
Can a figure be congruent to its mirror image?
Yes, a figure is congruent to its mirror image because it still has the same size and shape, even through it is flipped.
5. Can a figure be similar to a rotated or reflected version of itself?
Yes, a figure is still similar to a rotated or reflected version of itself because the shape remains the same and the sides are still in proportion.
5. What trigonometric ratio would you use to find a missing angle if you know the lengths of the opposite and adjacent sides?
You would use tangent (tan) and apply the inverse: tan-1 (opposite / adjacent) to find the angle.
5. A rectangular box is 5 cm long, 3 cm wide, and 2 cm high. What is its volume?
Volume = l x w x h = 5 x 3 x 2 = 30 cm3
5. A card is drawn from a standard deck of 52 cards. What is the probability that it is a queen?
There are 4 queens in a deck.
Probability = 4/52 = 1/13