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both names, every time

Lines of Symmetry · Grade 4 · 4.G.A.3

Name It Twice, Then Fold It

Name Date Correct / 30

1 Both names, then the folds. Name each figure by its sides and by its angles, then find its lines of symmetry. One name does not tell you the other.

Ring both names for every picture, then count the lines of symmetry it holds. Some are turned, so read the corner and not the way it sits.

1. (a)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

2. (b)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

3. (c)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

4. (d)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

5. (e)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

6. (f)

cornerrightacuteobtuse

sides3 alike2 alikenone alike

lines it holds

Roots of Reason

Name It Twice, Then Fold It · 4.G.A.3

Name Date

2 Which name decided it? Then ask the same question the other way around.

7. Look back at your six answers. One of the two names told you the count every time and the other never did on its own. Name each of them, and give two pictures with the same corner name and different counts.

Now the count comes first and the group is what you have to find. Ring one answer for each.

8. A triangle holds exactly 3 lines of symmetry.

so its sides are3 alike2 alikenone alikecannot tell

9. A triangle holds exactly 1 line of symmetry.

so its sides are3 alike2 alikenone alikecannot tell

10. A triangle holds no line of symmetry at all.

so its sides are3 alike2 alikenone alikecannot tell

11. A four sided figure holds exactly 2 lines of symmetry. Does that count tell you what kind of figure it is?

the counttells youdoes not tell you

Name two four sided figures that are not the same kind as each other and that each hold exactly 2. Say how you know each one holds 2.

Roots of Reason

Name It Twice, Then Fold It · 4.G.A.3

Name Date

3 Draw it, then turn it. Each triangle needs a right angle, and the two need different numbers of lines of symmetry.

12. Draw one triangle in each box. Both must have a right angle. Then draw every line of symmetry your triangle holds and write the count.

with exactly two sides alike

lines it holds

with no two sides alike

lines it holds

13. Picture (n) has been turned. Say what kind of figure it is, then rule and count every line of symmetry.

it isa squarenot a square

lines it holds

14. Neither side of (p) follows a line of dots. Count the steps along each side, then say how they meet.

the two sides meetat a right angleat a slant

Roots of Reason

Name It Twice, Then Fold It · 4.G.A.3

Name Date

3 Draw it, then turn it. Each triangle needs a right angle, and the two need different numbers of lines of symmetry.

15. A classmate drew 2 lines on picture (n) and stopped. Say which directions were never tried, and what they would have found.

Roots of Reason

rootsofreason.org

Answer Key

Lines of Symmetry · Grade 4 · 4.G.A.3

Name It Twice, Then Fold It

Both names, then the folds

1. (a) right, 2 alike, 1 2. (b) acute, 3 alike, 3 3. (c) obtuse, none alike, 0
4. (d) right, 2 alike, 1 5. (e) obtuse, 2 alike, 1 6. (f) right, none alike, 0
Pictures (a) and (d) are one triangle at two attitudes, so all three answers must agree. In (a) the line runs straight up the page. In (d) it leans, and a student who tries only across and down reports 0 and also calls the right angle acute.

Which name decided it

7. The side name decided it every time: a triangle with 3 equal sides has 3 lines of symmetry, one with 2 equal sides has 1, and one with no equal sides has 0. The corner name never did on its own. Accept (a) and (f), both right triangles with 1 and 0 lines, or (c) and (e), both obtuse with 0 and 1.
8. 3 alike 9. 2 alike 10. none alike
11. No. A rectangle that is not a square holds 2, one across and one up. A rhombus that is not a square holds 2, both corner to corner. The two are not the same kind of figure and the count cannot tell them apart. A square holds 4, so it is not one of the two.

Draw it, then turn it

12. Left box 1, right box 0. Both triangles have a right angle, so the corner name settled neither count and the side name decided both.
13. A square, holding 4 lines. Two run straight up and across the page through facing corners. Two lean, through the middles of facing sides.
14. At a right angle. One side steps 3 across and 2 up, the other 2 across and 3 down. Neither follows a line of dots and they still meet at a right angle, which is the crossing a line of symmetry has to make with the join between two matching corners.
15. The two leaning directions, through the middles of facing sides. They hold the other two lines, which makes 4.

Mark items 1 to 6 as three answers each. A student who ringed one name per picture and left the other blank is missing one idea, not making six separate mistakes: ask them for the missing name on (a) alone. A student who wrote 0 for (d) and 2 for (n) is missing a different one, and both are answered by turning the page rather than by counting again.