Which transformation slides every point of a figure by the same distance in the same direction? — Translation.A translation slides all points by the same vector (a, b), moving the figure without rotating or flipping it.
Which transformation flips a figure over a line? — Reflection.A reflection flips a figure over a line (axis of reflection), creating a mirror image.
Which transformation turns a figure around a fixed point? — Rotation.A rotation turns a figure by a given angle around a fixed center point.
Which transformation changes the SIZE of a figure? — Dilation.A dilation scales a figure by a factor k. If k ≠ 1, the size changes (k > 1 enlarges, 0 < k < 1 shrinks).
After a translation, the image is _____ to the original. — Congruent.Translations are rigid motions — they preserve all distances and angles. The image is congruent to the original.
Point A is at (2, 5). After translating by (3, −1), where is A'? — (5, 4).(2+3, 5+(−1)) = (5, 4).
Point (6, 0) is dilated by factor 1/2 about the origin. The image is at: — (3, 0).(1/2 × 6, 1/2 × 0) = (3, 0).
How many degrees does a half-turn rotation equal? — 180°.A half-turn is 180°. A full turn is 360°.
The Pythagorean Theorem states: — a² + b² = c².The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a, b are the legs.
In a right triangle, the hypotenuse is: — Opposite the right angle (longest side).The hypotenuse is always the longest side, opposite the right angle.
A right triangle has legs of 3 and 4. What is the hypotenuse? — 5.3² + 4² = 9 + 16 = 25. √25 = 5. Classic (3, 4, 5) Pythagorean triple.
A right triangle has legs of 5 and 12. What is the hypotenuse? — 13.5² + 12² = 25 + 144 = 169. √169 = 13. The (5, 12, 13) triple.
A right triangle has hypotenuse 10 and one leg 6. Find the other leg. — 8.6² + b² = 10² → 36 + b² = 100 → b² = 64 → b = 8.
What is the distance between (0, 0) and (3, 4)? — 5.d = √(3² + 4²) = √25 = 5.
What is the Pythagorean Theorem used to find? — Side lengths of a right triangle.The Pythagorean Theorem relates the three side lengths of a right triangle: a² + b² = c².
Two triangles are SIMILAR if: — They have the same shape (equal angles and proportional sides).Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional.
The AA Criterion for similarity states: — Two pairs of equal angles.AA (Angle-Angle): if two pairs of angles are equal, the triangles are similar. The third angle is forced to match since all angles sum to 180°.
Why does knowing only 2 angle pairs guarantee triangle similarity? — Two angles determine the third since all angles sum to 180°.Since triangle angles sum to 180°, knowing 2 angles determines the third. Two matching pairs guarantee all three match.
Triangle ABC has angles 50°, 60°, 70°. Triangle DEF has angles 50°, 70°, 60°. Are they similar? — Yes — AA criterion satisfied (same angles).Both triangles have the same angle set {50°, 60°, 70°}. Two angle pairs match → AA criterion → similar.
What notation is used to indicate similar triangles? — ∼.∼ (tilde) means "similar." ≅ means congruent. Note the order matters: △ABC ∼ △DEF means A↔D, B↔E, C↔F.
Two similar triangles have sides in ratio 2:3. If the smaller triangle has a side of 8, the corresponding side of the larger is: — 12.8 × (3/2) = 12. Multiply by the ratio to find the corresponding side.
To use AA similarity, you need: — 2 pairs of matching angles.AA requires exactly 2 pairs of equal angles (the third is determined automatically).
An exterior angle of a triangle equals: — The sum of the two non-adjacent (remote) interior angles.Exterior Angle Theorem: the exterior angle equals the sum of the two remote (non-adjacent) interior angles.
Two remote interior angles are 40° and 55°. What is the exterior angle? — 95°.Exterior angle = 40° + 55° = 95°.
Two remote interior angles are 70° and 30°. What is the exterior angle? — 100°.Exterior angle = 70° + 30° = 100°.
An exterior angle is 115° and one remote interior angle is 60°. What is the other remote interior angle? — 55°.115° = 60° + x → x = 55°.
An exterior angle is 130° and one remote interior angle is 70°. What is the other remote interior angle? — 60°.130° = 70° + x → x = 60°.
How does an exterior angle compare to each remote interior angle? — It is always larger than either one alone.The exterior angle equals the SUM of both remote angles, so it must be larger than either one individually.
The exterior angle at a vertex plus the interior angle at the same vertex equals: — 180°.The exterior angle and interior angle at the same vertex form a straight line (linear pair) and sum to 180°.
An exterior angle of 150° is created at one vertex. What is the interior angle at that same vertex? — 30°.Interior + exterior = 180°. Interior = 180° − 150° = 30°.
The volume formula for a cylinder is: — V = πr²h.V_cylinder = πr²h. The base area is πr², multiplied by height h.
The volume formula for a cone is: — V = (1/3)πr²h.V_cone = (1/3)πr²h. It is exactly one-third the volume of a cylinder with the same base and height.
The volume formula for a sphere is: — V = (4/3)πr³.V_sphere = (4/3)πr³. Remember the 4/3 fraction and that the radius is CUBED.
A cone's volume is what fraction of a cylinder with the same base and height? — 1/3.V_cone = (1/3)V_cylinder. Three cones fill exactly one cylinder.
A cylinder has radius 3 cm and height 5 cm. What is its volume in terms of π? — 45π cm³.V = π(3²)(5) = π(9)(5) = 45π cm³.
A sphere has radius 3. What is its volume in terms of π? — 36π.V = (4/3)π(3³) = (4/3)π(27) = 36π.
What units are used for volume? — Cubic units (m³).Volume measures 3D space and is expressed in cubic units (m³, cm³, in³, ft³).