Which of the following shapes are congruent? (Show two identical triangles.)
Triangles A and B—they have the same size and shape with matching sides and angles.
Are these two rectangles similar if their sides are 4 cm by 8 cm and 6 cm by 12 cm?
Yes, the side ratios are equal (1:2).
In a right triangle, identify the hypotenuse, opposite, and adjacent sides relative to angle A.
Hypotenuse = longest side, Opposite = across from angle A, Adjacent = next to angle A.
Find the surface area of a cube with side length 4 cm.
96 cm².
What is the probability of rolling a 3 on a six-sided die?
1/6. One favorable outcome out of six.
Prove the two triangles are congruent: Triangle ABC and Triangle DEF where AB = DE, BC = EF, and ∠B = ∠E.
Yes, by SAS (Side-Angle-Side). Two sides and the included angle are congruent.
In similar triangles, the small triangle has a side of 5 cm, and the corresponding side in the large triangle is 15 cm. If another side in the small triangle is 4 cm, what is the corresponding side in the large triangle?
12 cm. Scale factor = 3, so 4 × 3 = 12.
A right triangle has a leg of 3 units and a hypotenuse of 5 units. Find sin(θ).
sin(θ) = 3/5. Opposite over hypotenuse.
Find the volume of a cone with radius 3 cm and height 4 cm.
37.7 cm³
What is the probability of flipping two heads with two coins?
1/4. Only HH out of four outcomes.
Triangle XYZ is congruent to triangle LMN. If ∠X = 40°, ∠Y = 60°, and side XY = 5 cm, what is the measure of ∠M and the length of side LM?
∠M = 40°, LM = 5 cm. (Corresponding parts of congruent triangles are congruent.)
A map uses a scale of 1 inch = 5 miles. If two cities are 3 inches apart on the map, how far are they in real life?
15 miles. Multiply 3 × 5 = 15.
A ladder leans against a wall forming a 60° angle with the ground. The ladder is 10 ft long.
How high does it reach on the wall?
Use sin(60°) × 10.
8.66 ft.
A cylinder has radius 5 cm and height 10 cm. A cone with the same dimensions is removed. What is the volume of the remaining solid?
523.6cm3
iA bag has 3 red, 2 blue, and 5 green marbles. If you pick two without replacement, what’s the probability both are red?
1/15.