Grade 4 Geometry Practice — Hard

Question 1 of 27Score 0/0Hard

Question 1 of 27: Two angles in a triangle each measure 60°. What is the third angle?

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Keep going: Read the lesson: Lines, Line Segments, Rays & Angles
Answer key for parents & teachers (27 questions)
  1. Two angles in a triangle each measure 60°. What is the third angle?60°. Angles in a triangle add to 180°. 60° + 60° + third = 180°. Third = 180° − 120° = 60°.
  2. How many ANGLES does a pentagon have?5. A pentagon has 5 sides and exactly 5 interior angles (one at each vertex).
  3. A right angle and an acute angle together form an angle that is:Less than 180° (obtuse). Right (90°) + acute (< 90°) = between 90° and 180° — an obtuse angle!
  4. A REFLEX angle is:Greater than 180°. A REFLEX angle is greater than 180° (and less than 360°) — it is the "outside" angle.
  5. The sum of angles in a quadrilateral (4-sided figure) is:360°. Any quadrilateral can be split into 2 triangles. 2 × 180° = 360°. All interior angles sum to 360°.
  6. Which best describes a LINE in notation?AB with double-ended arrows over it. A line is written with double-ended arrows (↔) over the letters — indicating it extends infinitely in both directions.
  7. An angle is measured in:Degrees (°). Angles are measured in DEGREES (°). A full rotation is 360°.
  8. Which tool is used to measure angles precisely?Protractor. A PROTRACTOR is the tool for measuring angles in degrees.
  9. Two rays from the same vertex pointing in OPPOSITE directions form an angle of:180° (straight angle). Opposite rays form a straight line — a 180° STRAIGHT ANGLE.
  10. A hexagon — does it have any parallel sides?Yes — a regular hexagon has 3 pairs of parallel sides. A regular hexagon has 3 pairs of parallel opposite sides!
  11. Lines AB ∥ CD and AB ⊥ EF. What angle do CD and EF form?90°. AB ∥ CD means CD runs the same direction as AB. AB ⊥ EF means EF is 90° from AB. So CD is also 90° from EF!
  12. A square has parallel sides AND perpendicular sides. A regular hexagon has parallel sides but NO perpendicular sides. Why?Hexagon internal angles are 120°, not 90°, so no right angles between sides. Regular hexagon interior angles = 120°. Adjacent sides meet at 120°, not 90° — so no perpendicular adjacent sides.
  13. If line m is perpendicular to line n, and line n is perpendicular to line p, then m and p are:Parallel. If m⊥n and n⊥p, then m and p are PARALLEL (both at 90° to n means they point the same direction).
  14. How many pairs of parallel sides does a regular octagon have?4. A regular octagon has 4 pairs of parallel sides — each side is parallel to the one directly across from it.
  15. Which shape has BOTH pairs of opposite sides parallel AND all sides equal, but NOT all angles are right angles?Rhombus. A RHOMBUS has opposite sides parallel and all sides equal, but its angles are NOT all 90° (unless it is a square).
  16. In a coordinate grid, the x-axis and y-axis are:Perpendicular. The x-axis (horizontal) and y-axis (vertical) are PERPENDICULAR — they intersect at the origin at 90°.
  17. True or False: Every pair of perpendicular lines also intersects.True. TRUE. By definition, perpendicular lines MUST intersect (at 90°). Two lines that do not intersect cannot be perpendicular.
  18. Can two lines be both parallel AND perpendicular to each other at the same time?No — parallel means they never meet; perpendicular means they must meet at 90°. IMPOSSIBLE! Parallel = never meet. Perpendicular = must meet at 90°. A line cannot both never meet and meet another line!
  19. Which describes a shape with ZERO lines of symmetry?No fold creates two matching halves. A shape with ZERO lines of symmetry has no fold that creates matching halves — it is asymmetric!
  20. If a figure has a line of symmetry, the two halves are CONGRUENT (same shape and size). True or False?True. TRUE! The two halves of a symmetric figure are congruent — same shape, same size, mirror images of each other.
  21. An isosceles triangle (two equal sides) has how many lines of symmetry?1 (through the vertex between the equal sides). An isosceles triangle has EXACTLY 1 line of symmetry — the perpendicular bisector of the unequal side (from the apex down).
  22. A regular octagon has how many lines of symmetry?8. A regular octagon has 8 lines of symmetry (same as the number of sides for any regular polygon).
  23. Which transformation is most related to lines of symmetry?Reflection. A line of symmetry is the LINE OF REFLECTION — reflecting the shape across this line maps it perfectly onto itself.
  24. You fold a piece of paper and cut a shape. When you unfold, it has a line of symmetry. Where is the line?The fold line itself. The FOLD LINE is the line of symmetry! When you unfold, both halves are mirror images because the fold created symmetric cuts.
  25. How many lines of symmetry does the letter "X" have?2. The letter X has 2 lines of symmetry: one vertical (|) and one horizontal (−). Both divide it into matching halves.
  26. A figure has 6 lines of symmetry. It is most likely a:Regular hexagon. Regular hexagons have exactly 6 lines of symmetry (one from each vertex and one through each side midpoint).
  27. True or False: Every rectangle that is NOT a square has exactly 2 lines of symmetry.True. TRUE! A non-square rectangle has exactly 2 lines of symmetry — one horizontal through midpoints, one vertical through midpoints. The diagonals do NOT create symmetric halves.