4th Grade Lines, Rays and Classifying Shapes Worksheet Answer Key (PDF)

4th grade lines and angles worksheet answers – Maths PDF

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This 4th grade lines and angles worksheet answers covers lines, rays and classifying shapes (Common Core 4.G.A.1, 4.G.A.2), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students and parents check lines, angles, and shape classification work, with a reason shown for each answer.

Topic: Lines, Rays and Classifying Shapes (4th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 4.G.A.1, 4.G.A.2
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students and parents check lines, angles, and shape classification work, with a reason shown for each answer. Also, each solution names the property used, such as the number of endpoints, the angle size, or the pairs of parallel sides.

The key covers all 20 problems, including the table in problem 12 and the drawing instructions for problems 5 and 6. Then, word problem answers use full sentences. Also, when a shape could have two names, the key explains which name is the most exact. Then, plan about 15 minutes to check your answers and redo any that differ.

Each answer explains why, using the key words: endpoint, parallel, perpendicular, right, acute, and obtuse. The final answer is in bold. Drawing problems show a finished picture that you can compare with your own.

Grade 4 · Common Core State Standards: 4.G.A.1, 4.G.A.2

4th grade lines and angles worksheet answers: worksheet problems 1 to 10

1 – Name the figures

Two endpoints: line segment. One endpoint: ray. No endpoints and arrows both ways: line.

segment, ray, line

2 – Count the endpoints

A segment has 2, a ray has 1, and a line has 0.

2, 1, and 0

3 – Parallel or perpendicular

Opposite edges never meet: parallel.
A wall meets the floor at a right angle: perpendicular.
Rails stay the same distance apart: parallel.

parallel, perpendicular, parallel

4 – Name the angles

A is 55°, less than 90°: acute. B is 90°: right. C is 125°, more than 90°: obtuse.

A acute, B right, C obtuse

5 – Draw a segment

Draw a straight piece with a dot at each end and label the dots.

Segment MN.

Segment MN

6 – Draw perpendicular lines

Draw one line. Use the corner of a card to draw a second line that crosses it at 90°. Mark the square.

Perpendicular lines.

Two lines crossing at 90°

7 – Count the right angles

Each corner has a small square. There are 4 corners.

4 right angles

8 – Count parallel sides

The top and bottom sides are marked with arrows. The slanted sides are not parallel.

1 pair

9 – Classify triangles

All angles are less than 90°: acute.
It has a 90° angle: right.
It has a 120° angle, which is more than 90°: obtuse.

acute, right, obtuse

Worksheet problem 10 and after

10 – Is it a right triangle?

One corner has a small square, so it is a right angle.

Yes, it is a right triangle.

Worksheet problems 11 and up

11 – Name the quadrilateral

Four right angles make a rectangle. All sides equal makes it a square.

a square

12 – Complete the table

Rectangle: 2 pairs, 4 right angles.
Slanted parallelogram: 2 pairs, 0 right angles.
Trapezoid with slanted sides: 1 pair, 0 right angles.
Right triangle: 0 pairs, 1 right angle.

2 and 4; 2 and 0; 1 and 0; 0 and 1

13 – Always, sometimes, never

A square always has 4 right angles.
Two right angles leave no room for a third side, so never.
Some quadrilaterals, like rectangles, have right angles, and some, like slanted parallelograms, do not: sometimes.

always, never, sometimes

14 – Perpendicular corners

Each corner is a pair of sides meeting at 90°. A rectangle has 4 corners, so 4 pairs.

4 pairs

15 – City map

Main St and Oak St stay the same distance apart and never meet: parallel.

1st Ave crosses Main St at 90°: perpendicular.

City map.

Parallel: Main St and Oak St. Perpendicular: 1st Ave and Main St

16 – Picture frame

Four right angles and opposite sides parallel make a rectangle.

A square needs all sides equal, but 12 in is not 8 in.

A rectangle; no, it is not a square

17 – Wooden ramp

It has one 90° angle, so it is a right triangle.

30° and 60° are both less than 90°, so there are 2 acute angles.

Right triangle; 2 acute angles

Worksheet problem 18 and after

18 – Clock angles

2:00: hands are 2 numbers apart, \(2 \times 30 = 60\)°, acute.

3:00: \(3 \times 30 = 90\)°, right.

5:00: \(5 \times 30 = 150\)°, obtuse.

acute, right, obtuse

19 – Floor tiles

Four sides with two pairs of parallel sides: a parallelogram.

Also, a rectangle needs four right angles, and these tiles have none.

A parallelogram; not a rectangle

20 – Flag design

Rectangle: 4. Right triangle: 1. Trapezoid: 2.

\(4 + 1 + 2 = 7\).

Diego’s flag pieces.

7 right angles

Key facts behind this 4th grade lines and angles worksheet answers

Key facts

A line segment has two endpoints; a ray has one; a line has none.
Parallel lines never meet, and perpendicular lines meet at a right angle (90°).
Right angles are 90°, acute angles are less than 90°, and obtuse angles are greater than 90°.
Then, a right triangle has exactly one right angle.
Quadrilaterals are sorted by pairs of parallel sides and by right angles.

Common mistakes with this 4th grade lines and angles worksheet answers

Students accept any name for a shape that fits. The key gives the most exact name, such as rectangle instead of just quadrilateral.
Students check drawings in problems 5 and 6 by eye. Instead, use a card corner to confirm a right angle and a ruler to check that endpoints are labeled.
Students skip the reason in problem 10. Also, the key explains that a right angle in a triangle means it is a right triangle.
Students ignore the count in problem 20. Instead, add the right angles from each shape on the flag, including the trapezoid’s two.

How to use these solutions

Circle the property that decides each answer in the key, such as endpoints or 90 degrees. Then, learning to find that deciding property helps on tests.
Redo each missed problem by drawing the shape. Finally, a drawn picture often shows a property that a description hides.
Parents can ask the child to explain why a square is also a rectangle and a parallelogram. Repeat this habit on every problem for the best results.

Download the 4th grade lines and angles worksheet answers as a PDF with the button below and keep it with your notes.

4th grade lines and angles worksheet answers: frequently asked questions

Why is the answer to problem 19 a parallelogram?

The tile has four sides, opposite sides are parallel, and no angle is a right angle. That matches a parallelogram. It is not a rectangle, because a rectangle needs four right angles. A rhombus would also fit if all sides were equal.

How many right angles are on the flag in problem 20?

The rectangle has four right angles, the right triangle has one, and the trapezoid has two. Adding them gives seven right angles in all. Counting each shape separately and then adding keeps the work clear and easy to check.

What if my drawing of perpendicular lines looks slightly off?

Check it with the corner of a sheet of paper. If the corner fits snugly, the lines are perpendicular. Small differences are normal in freehand drawings, but marking the right angle with a small square shows that you meant it to be 90 degrees.

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