Plot A(2, 3) and B(5, 3). What is the horizontal distance between them? — 3 units.Same y-coordinate means they are on the same horizontal line. Horizontal distance = |5 − 2| = 3 units.
Plot C(4, 2) and D(4, 6). What is the vertical distance between them? — 4 units.Same x-coordinate means on the same vertical line. Vertical distance = |6 − 2| = 4 units.
A graph shows a rectangle with vertices at (1,1), (4,1), (4,3), (1,3). What is its width (horizontal)? — 3 units.Width = horizontal distance between x=1 and x=4 = 3 units.
In the rectangle above, what is its height (vertical)? — 2 units.Height = vertical distance between y=1 and y=3 = 2 units.
Which point lies on the x-axis? — (3, 0).Points ON the x-axis have y = 0. (3, 0) has y = 0, so it lies on the x-axis.
A treasure is buried at (7, 4). Starting from (0, 0), how far do you walk right and then up? — 7 right, 4 up.x = 7 (right), y = 4 (up). Walk 7 units right, then 4 units up!
Three points: A(1, 2), B(3, 4), C(5, 6). What pattern do you notice? — Each point increases by 2 in both x and y.Going from A to B: x +2, y +2. B to C: x +2, y +2. They lie on a straight line!
A point at (4, 0) is on which axis? — x-axis.y = 0 means the point lies on the x-axis.
True or False: All parallelograms are rectangles. — False — rectangles require right angles, but parallelograms do not.FALSE. A parallelogram just needs 2 pairs of parallel sides. For it to be a rectangle, it also needs 4 right angles.
True or False: All rectangles are parallelograms. — True.TRUE. Every rectangle has 2 pairs of parallel sides, so it meets the definition of a parallelogram.
Which pair shows a shape and a MORE GENERAL category it belongs to? — Rectangle → trapezoid.Rectangle → trapezoid is correct: every rectangle has at least 1 pair of parallel sides, so it qualifies as a trapezoid. The rectangle is more specific.
A shape has 4 sides, 2 pairs of parallel sides, 4 equal sides, and NO right angles. It is a: — Rhombus.Equal sides + 2 pairs parallel sides + NO right angles = RHOMBUS (not a square, which requires right angles).
In the hierarchy, which is more GENERAL (broader): parallelogram or rectangle? — Parallelogram.Parallelogram is MORE GENERAL — it includes rectangles, rhombuses, and squares. Rectangle is a special parallelogram.
A rhombus with all right angles is a: — Square.Rhombus (4 equal sides) + right angles (4 × 90°) = SQUARE!
Does a trapezoid belong to the parallelogram category? — No — a trapezoid has only 1 pair of parallel sides, not 2.A trapezoid has only ONE pair of parallel sides. A parallelogram needs TWO. Trapezoid is NOT a parallelogram (by most definitions).
How many pairs of parallel sides does a square have? — 2.A square has 2 pairs of parallel sides: top∥bottom and left∥right. That is why it is a parallelogram!
A triangle has angles 50° and 70°. What is the third angle? — 60°.180° − 50° − 70° = 60°.
An equilateral triangle has angles 60°, 60°, 60°. What TYPE by angles is it? — Acute.All angles are 60° — all less than 90°. So it is an ACUTE triangle!
Can a triangle have two right angles? — No — two 90° angles would already equal 180°, leaving 0° for the third.90° + 90° = 180°. The third angle would need to be 0°, which is impossible. A triangle can have AT MOST one right angle.
A triangle has sides 5, 5, and 8. What type is it by SIDES? — Isosceles.Two sides are equal (5 and 5). One side is different (8). So it is ISOSCELES.
A triangle has sides 3, 4, and 5. Using the Pythagorean theorem: 3²+4²=5². What type is it by ANGLES? — Right.3²+4²=9+16=25=5². When a²+b²=c², the triangle is a RIGHT triangle!
The sum of angles in any POLYGON with n sides equals: — 180° × (n − 2).Angle sum of a polygon = 180° × (n − 2). Triangle: 180×1=180°; Quadrilateral: 180×2=360°.
What is the sum of interior angles in a PENTAGON (5 sides)? — 540°.180° × (5 − 2) = 180° × 3 = 540°.
Can a triangle be BOTH isosceles AND obtuse? — Yes — a triangle can be classified by both sides and angles simultaneously.YES! Classifications by sides (equilateral/isosceles/scalene) and angles (acute/right/obtuse) are INDEPENDENT — a triangle can be both isosceles AND obtuse!