4th Grade · 4.G.A.1

Types of angles in 4th grade

The three types of angles your child learns in 4th grade are right, acute and obtuse. Along with angles, your child draws and names points, lines, line segments and rays, and finds parallel and perpendicular lines inside shapes.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

What it means, in plain words

A point is an exact spot, shown as a dot. A line is perfectly straight and goes on forever in both directions, so it is drawn with an arrow at each end. A line segment is a piece of a line with two endpoints, like the edge of a ruler. A ray starts at one point and goes on forever in one direction, like the beam of a flashlight.

An angle is two rays that start at the same point. The types of angles in 4th grade are named by comparing them with a square corner, like the corner of a sheet of paper. A right angle is exactly a square corner. An acute angle is narrower than a square corner. An obtuse angle is wider than a square corner but not as wide as a straight line.

Parallel lines run side by side and never meet, like the two rails of a train track. Perpendicular lines meet or cross at a right angle, like the two lines of a plus sign. Your child finds all of these inside shapes too, such as the square corners and parallel sides of a rectangle.

Your child should be able to:

Draw and name a point, a line, a line segment and a ray
Sort angles into right, acute and obtuse by comparing them with a square corner
Draw parallel lines and perpendicular lines
Find right angles and parallel sides inside a shape

Example

What type of angle do the hands of a clock make at 3:00, at 2:00 and at 5:00?

At 3:00 the hands make a square corner, so it is a right angle.
At 2:00 the hands are closer together than at 3:00, so it is an acute angle.
At 5:00 the hands are wider apart than at 3:00 but not in a straight line, so it is an obtuse angle.
The angle is right at 3:00, acute at 2:00 and obtuse at 5:00.

Example

Which parts of the capital letter H are parallel, and which are perpendicular?

The two tall strokes run side by side and never meet, so they are parallel.
The crossbar meets each tall stroke at a square corner, so it is perpendicular to both.
The letter H has one pair of parallel line segments and a crossbar perpendicular to both of them.

Where children usually get stuck

Your child says an angle with long sides is bigger than an angle with short sides, even when the short one opens wider.
Bigger usually means longer, so your child measures the sides. The size of an angle is how far it opens, and the sides can be drawn any length.
What helps. Open two pencils into a V on the table. Swap them for two longer pencils at the same opening and ask whether the angle changed.
Your child draws a line as a short stroke with no arrows, or calls a line segment a line.
In everyday speech, any straight mark is a line. In math, a line goes on forever, and the arrows are how a drawing shows that.
What helps. Draw a line, a line segment and a ray side by side. Ask which one has an end, which has two ends and which has none.
Your child finds perpendicular lines only when one goes straight up and the other lies flat, and misses a tilted square corner.
Most pictures in books show right angles sitting square with the page, so the idea gets tied to how the corner is turned.
What helps. Use the corner of an index card as a tester. Hold it against tilted corners around the house and check which ones match.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Look at the figure below. Use the dropdowns to complete each statement about the figure.
The figure is
.
It has
.
It also has
.
Show the answer and how to solve it
The figure is a straight object with 2 endpoints and 0 arrows. A dot at each end shows where it stops — this is a line segment.
1. 1Look at the highlighted figure.
2. 2Decide if the figure is just one location (a single small dot) or a straight object with length. The figure stretches from the left end to the right end, so it is a straight object — not just one location.
3. 3Next, count the endpoints — the dots that show where the figure stops. There is a dot at the left end and a dot at the right end. So it has 2 endpoints.
4. 4Now count the arrows — the arrowheads that show the figure keeps going past what is drawn. There are no arrowheads on this figure. So it has 0 arrows.
5. 5Putting it together: the figure is a straight object with 2 endpoints and 0 arrows. A straight object that stops at both ends is a line segment.
Common mistake. A common mistake is counting only 1 endpoint and missing the second. Both the left end and the right end have dots, so be sure to count both endpoint dots.
The idea underneath. A dot at the end means the figure stops there. An arrow at the end means the figure keeps going past what you can see. Count dots and arrows separately to describe the figure.
2On level
Liam wants to draw a line through two marked points, A and B. His drawing is shown below. Select the statement that best describes Liam's drawing.
A
Liam's drawing is correct; the line passes through both marked points and extends in both directions.
B
Liam's line extends in both directions, but it passes through only one of the marked points.
C
Liam's drawing is not a line because it does not extend in both directions.
D
Liam's line extends in both directions, but it does not pass through either marked point.
Show the answer and how to solve it
Liam's drawing IS a line that extends in both directions, but it passes through only point A and misses point B by 2 grid units. To meet the goal, the line must pass exactly through both marked points.
1. 1First, look at Liam's drawing. To meet the goal, his line must pass exactly through both marked points, A and B.
2. 2Liam's drawing has arrows on both ends, so it IS a line that extends in both directions. It is not a segment (which would have two endpoints) or a ray (which would have one endpoint and one arrow).
3. 3Look at point A. Liam's line passes exactly through point A.
4. 4Look at point B. Liam's line does NOT pass through point B — it passes 2 grid units above B.
5. 5Liam's line passes through point A but not point B. This matches the statement that says his line extends in both directions but passes through only one of the marked points.
Common mistake. A common mistake is to focus only on whether the line goes near both points without checking that it passes exactly through each one. Liam's line goes close to point B but is shifted 2 grid units above it — close, but not the same as passing through B.
The idea underneath. A line drawn through two given points must pass exactly through BOTH points and extend in both directions. Going near a point — even by just one grid unit — is not the same as passing through it.
3On level
A student tried to find all the right angles in the figure below.
$\displaystyle \text{The student selected: } \angle B, \angle D$
Which statement best describes the student's work?
A
The student chose an angle that is not a right angle.
B
The student's choices are correct.
C
The student missed a right angle and chose an angle that is not a right angle.
D
The student missed a right angle.
Show the answer and how to solve it
The figure has $2$ right angles: $\angle B$ (horizontal and vertical sides) and $\angle D$ (a tilted square corner). The student selected exactly $\angle B$ and $\angle D$ , so the student's choices are correct. The best description is "The student's choices are correct."
1. 1Look at the figure. It has $4$ corners labeled $\angle A$ , $\angle B$ , $\angle C$ , and $\angle D$ . The goal is to find which corners are right angles (square corners).
2. 2Check $\angle A$ . The two sides meeting at $A$ form an acute angle — narrower than a square corner. $\angle A$ is NOT a right angle.
3. 3Check $\angle B$ . The bottom side (horizontal) and the right side (vertical) meet at a square corner. $\angle B$ IS a right angle.
4. 4Check $\angle C$ . The vertical side and the slanted upper side meet at an obtuse angle — wider than a square corner. $\angle C$ is NOT a right angle.
5. 5Check $\angle D$ . Both sides meeting at $D$ are tilted on the page, but they still form a square corner. $\angle D$ IS a right angle, even though it is tilted.
6. 6The right angles in the figure are $\angle B$ and $\angle D$ . The student selected exactly $\angle B$ and $\angle D$ , so the student's choices are correct.
Common mistake. A common mistake is to stop after the obvious horizontal-vertical corner and miss the tilted one. Here the student found both: $\angle B$ (upright) and $\angle D$ (tilted but still square).
The idea underneath. A right angle is two sides meeting at a square corner. The square corner can be tilted at any angle on the page — what matters is whether the two sides meet at a square corner, not whether they line up with horizontal and vertical.
4Stretch
Aaron was asked to make an obtuse angle. The angle is shown below.
Select the statement that best describes Aaron's angle.
A
Aaron made a right angle, not an obtuse angle.
B
Aaron made an obtuse angle.
C
Aaron's rays are too short to be an obtuse angle.
D
Aaron made an acute angle, not an obtuse angle.
Show the answer and how to solve it
Aaron made an acute angle, not an obtuse angle. The angle clearly opens narrower than $90^{\circ}$ , so it falls in the acute category.
1. 1Look at the angle Aaron made. The angle clearly opens narrower than $90^{\circ}$ .
2. 2The angle opens narrower than $90^{\circ}$ , so it is an acute angle.
3. 3There are three angle categories: acute (less than $90^{\circ})$ , right (exactly $90^{\circ})$ , and obtuse (greater than $90^{\circ})$ . An acute angle is not obtuse.
4. 4Aaron was asked to make an obtuse angle, but he made an acute angle. So his angle is not what was asked for.
Common mistake. A common mistake is confusing acute and obtuse angles. Acute angles open less than $90^{\circ}$ , while obtuse angles open more than $90^{\circ}$ .
The idea underneath. Angles fall into three categories: acute (less than $90^{\circ})$ , right (exactly $90^{\circ}$ , marked with a small square), and obtuse (greater than $90^{\circ})$ . A right angle is its own category — it is not acute and it is not obtuse.