Geometry

Use this for “M is the midpoint of AC, AM = 3x + 1 and MC = 5x − 7. Find x, AM and AC.”

Use this for “m∠AOB = 38° and m∠BOC = 47°. Find m∠AOC.”

Use this for “AB is 6 cm and the compass is open to 4 cm. How far above AB do the arcs cross?”

Use this for “What is the next step in constructing the perpendicular bisector of AB?”

Use this for “Put the steps for bisecting ∠AOB with a compass in order.”

Use this for “After bisecting ∠AOB with a compass, which statements must be true?”

Use this for “How can you find the center of a circle with a compass and straightedge?”

Use this for “Side BC is extended to D. m∠A = 52° and m∠B = 71°. Find m∠ACD and m∠ACB.”

Use this for “Given AB = AC, prove ∠B = ∠C” and “An isosceles triangle has a 40° vertex angle. What are its base angles?”

Use this for “Write the converse of ‘If two angles are vertical, then they are congruent.’ Is it true?”

Use this for “Is this conclusion reached by inductive or deductive reasoning?”

Use this for “Solve 2(x − 3) = 14 and give a reason for each step.”

Use this for “ℓ ∥ m and m∠1 = 118°. Find m∠3 and m∠6.”

Use this for “ℓ ∥ m and m∠4 = 73°. Find m∠6.”

Use this for “m∠1 = 81° and m∠5 = 79°. Are lines ℓ and m parallel?”

Use this for “ℓ ∥ m, corresponding angles are (4x + 12)° and (2x + 50)°. Find x and the angle.”

Use this for “Write the equation of the line parallel to y = 3x − 4 through (2, 7).”

Use this for “Write the equation of the line perpendicular to y = 2x + 1 through (4, 3).”

Use this for “Prove that the angles of a triangle add to 180°.”

Use this for “Translate A(1, 2) 5 units right, then reflect it across the x-axis.”

Use this for “Rotate A(6, 2) 90° counterclockwise about the point (1, 1).”

Use this for “Reflect A(4, 1) across the line y = x” or “across y = −x.”

Use this for “Which rotations carry a 6 by 4 rectangle onto itself? How many lines of symmetry does it have?”

Use this for “Is (x, y) → (2x, 2y) a rigid motion? Which move is (x, y) → (−y, x)?”

Use this for “△ABC ≅ △DEF, AB = 3x + 2 and DE = 2x + 8. Find x and AB.”

Use this for “△ABC ≅ △KLM. Which parts must be congruent?”

Use this for “M is the midpoint of PQ and of RS. Prove PR ≅ QS.”

Use this for “The median AD is 12. How long are AG and GD?”

Use this for “A right triangle has legs 9 and 12. Find the radius of the circle inside it.”

Use this for “A right triangle has legs 5 and 12. Find the radius of the circle through its corners.”

Use this for “Two sides of a triangle are 7 and 11. What lengths can the third side be?”

Use this for “Which point of a triangle is the same distance from all three sides?”

Use this for “A triangle has sides 5, 7 and 9. Which angle is the largest? The smallest?”

Use this for “In parallelogram ABCD, m∠A = 58°. Find m∠B and m∠C.”

Use this for “A rectangle is 12 by 5. How long is each diagonal?”

Use this for “A rhombus has diagonals 12 and 16. Find its side and its area.”

Use this for “A trapezoid has bases 9 and 15 and height 5. Find its midsegment and area.”

Use this for “A kite’s diagonals cross at O; BD = 12, OA = 8 and OC = 4.5. How long are its sides?”

Use this for “A regular hexagon has sides of 4 cm. Find its apothem and its area.”

Use this for “A parallelogram has perpendicular diagonals. What is the most exact name for it?”

Use this for “Dilate an 8 by 6 rectangle by a scale factor of 0.5 from the point O.”

Use this for “DE ∥ BC, AD = 6, DB = 4 and AE = 9. Find EC.”

Use this for “DE ∥ BC, AD = 3, AB = 12 and BC = 20. How long is DE?”

Use this for “D is on AB and E is on AC; AD = 4, DB = 6, AE = 6 and EC = 9. Is DE parallel to BC?”

Use this for “A 3 by 4 rectangle is enlarged by 2.5. What are the new perimeter and area?”

Use this for “The altitude to the hypotenuse cuts it into 4 and 9. How long is the altitude?”

Use this for “Which pairs of triangles must be similar, and why?”

Use this for “A leg of a 45°-45°-90° triangle is 7. How long is the hypotenuse?”

Use this for “The short leg of a 30°-60°-90° triangle is 5. Find the long leg and the hypotenuse.”

Use this for “A 7.5 m ladder leans at 38° to the ground. How high up the wall does it reach?”

Use this for “A ramp rises 1.5 m over a run of 6 m. What angle does it make with the ground?”

Use this for “Standing 36 m from a tree, you look up 28° to its top. How tall is the tree?”

Use this for “sin 28° is about 0.4695. Which cosine is equal to it?”

Use this for “b = 7, c = 10 and A = 50°. Find a.”

Use this for “The sides are 5, 7 and 9. Find the largest angle.”

Use this for “A = 30°, a = 6 and b = 10. How many triangles fit, and what is B?”

Use this for “Two sides of a triangle are 8 and 11 with a 40° angle between them. Find its area.”

Use this for “Find the midpoint of the segment from (−4, 3) to (8, −5)” or “M is the midpoint; find the other end.”

Use this for “Find the point P on AB, A(−2, 1) and B(10, 7), with AP:PB = 1:2.”

Use this for “Show that A(−3, −1), B(−1, 3), C(5, 4), D(3, 0) is a parallelogram.”

Use this for “Is the triangle A(−1, 1), B(1, 5), C(5, 3) a right triangle?”

Use this for “Find the perimeter and area of the triangle A(0, 0), B(6, 0), C(3, 4).”

Use this for “AB is a diameter and m∠PAB = 34°. Find m∠PBA.”

Use this for “The radius is 8 and the tangent from P is 15. How far is P from the center?”

Use this for “Chords AB and CD cross at E; AE = 6, EB = 4 and CE = 3. Find ED.”

Use this for “From P, PA = 3 and PB = 10 on one secant, PC = 5 on the other. Find PD.”

Use this for “From P, PA = 4 and PB = 16 on a secant. How long is the tangent PT?”

Use this for “ABCD is inscribed in a circle and m∠A = 84°. Find m∠C.”

Use this for “Two chords cross inside a circle, cutting off arcs of 70° and 110°. Find the angle.”

Use this for “Find the center and radius of x² + y² − 6x + 4y − 12 = 0.”

Use this for “A circle has center (1, 2) and radius 5. Find x when the point (x, 5) is on it.”

Use this for “A sector has radius 4 cm and central angle 2.5 radians. Find its arc length and area.”

Use this for “Find the surface area of a can with radius 4 cm and height 7 cm.”

Use this for “A cone has radius 3 cm and height 4 cm. Find its volume.”

Use this for “A cone has radius 3 cm and height 4 cm. Find its slant height and surface area.”

Use this for “A square pyramid has base side 6 cm and height 10 cm. Find its volume.”

Use this for “A ball has radius 5 cm. Find its surface area and volume.”

Use this for “A cone has radius 6 cm and height 9 cm. What is the area of a level cut 3 cm up?”

Use this for “A square pyramid has base side 6 cm and height 4 cm. Find its slant height and surface area.”

Use this for “A plane cuts a cube through three corners. What shape is the cross section?”

Use this for “A right triangle is turned about one leg. What solid does it sweep out?”

Use this for “A steel ball has radius 1.5 cm and steel is 7.8 g/cm³. Find its mass.”

Use this for “A solid aluminum cone (2.7 g/cm³) has radius 3 cm and height 4 cm. Find its mass.”

Use this for “45,000 people live within 3 km of a town’s center. How many people per km²?”

Use this for “A can must hold 500 cm³. Which radius uses the least metal?”

Use this for “40 m of fence makes a rectangular pen. Which sides give the most area?”

Use this for “P(red) = 0.25 and P(blue) = 0.40 for one marble. Find P(red or blue).”

Use this for “The chance of rain is 0.35. What is the chance of no rain?”

Use this for “Of 40 students, 22 play soccer, 15 basketball and 8 both. How many play neither, and what is the chance of neither?”

Use this for “Three coins are tossed. What is the chance of exactly two heads?”

Use this for “In how many ways can 8 runners take gold, silver and bronze?”

Use this for “In how many ways can a committee of 3 be chosen from 8 people?”

Use this for “3 students are picked at random from 5 girls and 4 boys. What is the chance all 3 are girls? Exactly 2?”

Use this for “P(Rain) = 0.3, P(Late | Rain) = 0.4, P(Late | Dry) = 0.1. Find P(Late) and P(Rain | Late).”

Use this for “Three trains are on time with chances 0.9, 0.8 and 0.7. What is the chance all three are? That at least one is late?”

Use this for “A bag has 5 red and 3 blue marbles. Two are drawn without putting the first back. Find P(red, then red).”

Use this for “Of 60 students, 25 drink juice, 30 milk and 10 both. What fraction of the juice drinkers drink milk?”