Grade 5 Geometry Practice ā€” Hard

Question 1 of 27Score 0/0Hard

Question 1 of 27: Point P is at (3, 5). If you move it 2 units to the right and 3 units down, where is it?

More Grade 5 practice

Keep going: Read the lesson: Graphing on the Coordinate Plane
Answer key for parents & teachers (27 questions)
  1. Point P is at (3, 5). If you move it 2 units to the right and 3 units down, where is it? ā€” (5, 2). Right: 3 + 2 = 5. Down: 5 āˆ’ 3 = 2. New point: (5, 2).
  2. Points A(2, 1), B(5, 1), C(5, 4), D(2, 4) form what shape? ā€” Rectangle. The width = |5āˆ’2|=3, height = |4āˆ’1|=3. All angles are right angles ā†’ it is a square (special rectangle)!
  3. What is the perimeter of the rectangle in the previous question? ā€” 12 units. Width = 3, height = 3. Perimeter = 2(3+3) = 12 units.
  4. A line passes through (0, 0) and (4, 4). Every point on this line has what property? ā€” x = y. Both points have equal x and y values (0=0, 4=4). Every point on this line has x = y!
  5. Plot points (1,3), (2,3), (3,3), (4,3). They form a: ā€” Horizontal line. All points have y = 3, but different x values ā†’ they form a HORIZONTAL line at y = 3.
  6. You plot: (2, 1), (4, 2), (6, 3), (8, 4). The y-values are half the x-values. If x = 10, y = ? ā€” 5. Pattern: y = x/2. If x = 10, then y = 10/2 = 5. The point is (10, 5).
  7. The area of a rectangle with corners at (2,1), (6,1), (6,4), (2,4) is: ā€” 12 sq units. Width = 6āˆ’2 = 4. Height = 4āˆ’1 = 3. Area = 4Ɨ3 = 12 sq units.
  8. What is the distance between (1, 1) and (4, 5)? (Hint: use the Pythagorean theorem) ā€” 5 units. Horizontal change = 3, vertical change = 4. Distance = āˆš(3Ā²+4Ā²) = āˆš(9+16) = āˆš25 = 5 units.
  9. Which ordered pair is NOT in the first quadrant (x>0, y>0)? ā€” (0, 4). (0, 4) has x = 0, which is on the y-axis ā€” not strictly inside the first quadrant (which requires x > 0 AND y > 0).
  10. In the shape hierarchy, the ORDER from most specific to most general for quadrilaterals is: ā€” Square ā†’ rectangle ā†’ parallelogram ā†’ trapezoid ā†’ quadrilateral. Most specific (most requirements) to most general (fewest requirements): Square ā†’ Rectangle ā†’ Parallelogram ā†’ Trapezoid ā†’ Quadrilateral.
  11. True or False: Every square is also a rhombus. ā€” True. TRUE! A rhombus requires 4 equal sides. A square has 4 equal sides. So every square is a rhombus!
  12. Can a shape be BOTH a rhombus AND a rectangle? ā€” Yes ā€” it would be a square. Rhombus (4 equal sides) + Rectangle (4 right angles) = SQUARE. A square is simultaneously a rhombus AND a rectangle!
  13. Which property do ALL parallelograms share? ā€” Opposite sides are parallel and equal. ALL parallelograms have opposite sides that are both parallel AND equal in length. This is the defining property.
  14. Why is a square the "most specific" quadrilateral? ā€” It has the MOST requirements: equal sides + right angles + parallel sides. A square must satisfy ALL of: 4 equal sides, 4 right angles, 2 pairs of parallel sides. More requirements = more specific = smaller category.
  15. A shape belongs to the rectangle class but NOT the rhombus class. What can we conclude? ā€” It has right angles but NOT all 4 sides equal. Rectangle = 4 right angles. Rhombus = 4 equal sides. If rectangle but NOT rhombus, it has right angles but NOT all equal sides ā€” just a regular rectangle!
  16. The "shape hierarchy" reflects which mathematical concept? ā€” Set theory ā€” specific sets are subsets of more general sets. Shape hierarchy is SET THEORY: squares are a SUBSET of rectangles, which are a SUBSET of parallelograms, etc.
  17. How many quadrilaterals are also parallelograms? (Think about: are all quadrilaterals parallelograms?) ā€” Only those with 2 pairs of parallel sides. NOT all quadrilaterals are parallelograms. Only those with 2 pairs of parallel sides qualify. Trapezoids and irregular quadrilaterals are not parallelograms.
  18. If shape A is a square, which of these is FALSE: "A is a rectangle" / "A is a parallelogram" / "A is a triangle"? ā€” A is a triangle. A square is a rectangle and a parallelogram ā€” those are TRUE. But a square is a QUADRILATERAL (4 sides), not a triangle (3 sides) ā€” that is FALSE.
  19. An equilateral triangle has 3 lines of symmetry. An isosceles triangle has: ā€” 1. An isosceles triangle has exactly 1 line of symmetry ā€” through the apex and midpoint of the base.
  20. What is the sum of interior angles of a HEXAGON (6 sides)? ā€” 720Ā°. 180Ā° Ɨ (6 āˆ’ 2) = 180Ā° Ɨ 4 = 720Ā°.
  21. A regular polygon has all angles equal. Each interior angle of a regular hexagon is: ā€” 120Ā°. Sum = 720Ā°. 6 equal angles: 720Ā° Ć· 6 = 120Ā° each.
  22. Triangle ABC: angle A = 3x, angle B = 2x, angle C = x. Solve for x. ā€” x = 30Ā°. 3x + 2x + x = 6x = 180Ā°. x = 30Ā°. Angles are 90Ā°, 60Ā°, 30Ā°.
  23. The triangle in the previous question (90Ā°, 60Ā°, 30Ā°) is what type by ANGLES? ā€” Right. It has one 90Ā° angle ā†’ RIGHT triangle.
  24. What is the measure of each interior angle of a REGULAR OCTAGON (8 sides)? ā€” 135Ā°. Sum = 180Ā°Ć—(8āˆ’2) = 180Ā°Ć—6 = 1080Ā°. Each angle: 1080Ā°Ć·8 = 135Ā°.
  25. An exterior angle of a triangle equals the sum of: ā€” The two non-adjacent interior angles. The exterior angle of a triangle = sum of the two REMOTE interior angles (not the adjacent one).
  26. A triangle has one angle of 110Ā°. It is classified as: ā€” Obtuse triangle. 110Ā° > 90Ā°, so there is one obtuse angle ā†’ OBTUSE triangle.
  27. What polygon can be divided into exactly 4 triangles by drawing diagonals from one vertex? ā€” Hexagon. From one vertex, you can draw diagonals to all non-adjacent vertices. A hexagon has 6 sides ā†’ 6āˆ’2=4 triangles. Formula: nāˆ’2 triangles.