Geometry and Angles: math practice, Grade 4 – download the PDF

1 Line, ray or segment? ★★★

Name each figure: line, ray or segment.

1. It has two endpoints and you can measure its length.
2. It starts at a point and goes on forever in one direction.
3. It has no endpoints and goes on forever both ways.

2 Segments on a line ★★★

Four points P, Q, R and S lie on a line, in that order. How many different segments can you name using two of these points as endpoints? List them.

3 Name the angle ★★★

Classify each angle as acute, right, obtuse or straight: 35°, 90°, 112°, 89°, 180°, 151°.

4 True or false in everyday life ★★★

Say whether each statement is true or false and explain why.

1. The two rails of a straight railroad track are parallel.
2. The hands of a clock at 3:00 form a right angle.
3. The hands of a clock at 6:00 form an acute angle.

5 Reading the protractor ★★★

The base ray of the protractor points to 0 on the outer scale.

(a) What is the measure of the angle? (b) Is it acute, right or obtuse?

6 Right angles and parallel sides ★★★

Copy and complete the table.

7 Counting lines of symmetry ★★★

How many lines of symmetry does each shape have? (a) a square (b) a rectangle that is not a square (c) an isosceles triangle that is not equilateral (d) an equilateral triangle (e) a triangle whose three sides all have different lengths.

8 Missing angle in a corner ★★★

Find the missing measure.

1. A right angle is split into 24° and an unknown angle.
2. Two angles on a straight line: one measures 128°. Find the other.
3. A right angle is split into 66° and an unknown angle.

9 Opening a door ★★★

A door is pushed open 25°, then pushed 40° farther. (a) How wide is the opening now? (b) How many more degrees are needed to open it a full right angle?

10 Triangles by sides ★★★

Classify each triangle as equilateral, isosceles or scalene from its side lengths (in centimeters): (a) 5, 5, 5 (b) 7, 7, 3 (c) 4, 5, 6 (d) 6, 9, 6.

11 Triangles by angles ★★★

The three angles of each triangle are given. Classify it as acute, right or obtuse. (a) 60°, 60°, 60° (b) 90°, 45°, 45° (c) 100°, 40°, 40° (d) 70°, 50°, 60°. Check that each triple adds up to 180°.

12 Quadrilateral true or false ★★★

True or false? Justify each answer.

1. Every square is a rectangle.
2. Every rectangle is a square.
3. A rhombus has four equal sides.
4. A trapezoid has exactly two pairs of parallel sides.

13 Clock angles ★★★

The hour marks on a clock are 30° apart. Find the angle between the hands at (a) 2:00 (b) 4:00 (c) 9:00 (d) 5:00, then classify each angle.

14 A wide angle ★★★

The base ray points to 0 on the outer scale.

(a) Measure the angle. (b) What kind of angle is it? (c) How many degrees more would make it a straight angle?

15 Letters and symmetry ★★★

Which of the capital letters A, B, E, F, H, M, R, T have (a) a vertical line of symmetry? (b) a horizontal line of symmetry?

16 Parallel or perpendicular streets ★★★

Use the map.

(a) Which two streets are parallel? (b) Which pairs of streets are perpendicular? (c) Is Pine Street parallel or perpendicular to any other street?

17 Adjacent angles ★★★

A big angle of 125° is split by a ray into a 47° angle and an unknown angle.

Find the unknown angle and classify all three angles.

18 Laptop screen ★★★

A laptop screen is open 105°. You close it 38°, then a friend opens it 21° more. (a) What is the final angle? (b) Is it acute, right or obtuse?

19 Pie chart angles ★★★

A circle is cut into four sectors at the school fair: the sectors measure 90°, 120°, 85° and an unknown angle. A full turn is 360°. (a) Find the fourth angle. (b) Which sector is obtuse?

20 Who am I? ★★★

Name the quadrilateral.

1. I have four equal sides and four right angles.
2. I have four equal sides but my angles are not right angles.
3. I have exactly one pair of parallel sides.
4. I have four right angles but my sides are not all equal.

21 Robot turns ★★★

A robot turns 40°, then 75°, then 65° in the same direction. (a) What is the total turn? (b) What fraction of a full 360° turn is that? Name the kind of angle it makes.

22 Find the mistake ★★★

Maya measures this angle and says “It is 130°”. The base ray points to 0 on the outer scale.

Explain her mistake and give the correct measure.

23 Folding a banner ★★★

A rectangular banner is 12 in by 8 in. It is folded exactly along a line of symmetry. (a) What are the two possible sizes of the folded banner? (b) Is the area of the folded banner the same in both cases?

24 Describe a triangle ★★★

A triangle has angles of 120°, 30° and 30°. The two sides next to the 120° angle each measure 6 cm. Classify it by its sides and by its angles.