Complete the Patterns worksheet for identifying and continuing shape sequences.

Let’s solve each row one by one. We’re looking for a repeating pattern in each row, and we need to fill in the two blank spots so the pattern continues correctly.

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Row 1:
□ _ △ _ □ △ △ □

Look at what’s given:
Positions: 1=□, 3=△, 5=□, 6=△, 7=△, 8=□

Try to find a repeating group. Let’s test if it repeats every 4 shapes:

If pattern is: □ △ △ □ → then next should be same again.

Check:
- Positions 1–4: □ ? △ ? → If we put △ in pos2 and △ in pos4? Wait, that would be □ △ △ △ — doesn’t match later.

Wait — look at positions 5–8: □ △ △ □ → That looks like a complete set!

So maybe the pattern is: □ △ △ □, repeating.

Then positions 1–4 should also be: □ △ △ □

But position 3 is already △ — good.

Position 1 is □ — good.

So position 2 should be △, position 4 should be □? But wait — let’s check:

If full pattern is □ △ △ □ | □ △ △ □

Then:

Pos1: □
Pos2: △ ← first blank
Pos3: △ (but image shows △ here — OK)
Wait no — in the image, row 1 is:

□ _ △ _ □ △ △ □

So pos3 is △, but if pattern is □ △ △ □, then pos3 should be △ — yes.

But pos2 is blank, pos4 is blank.

If pattern is □ △ △ □, then:

Pos1: □
Pos2: △ ← fill this
Pos3: △ ← matches
Pos4: □ ← fill this
Then pos5: □ — matches start of next group
pos6: △
pos7: △
pos8: □ — perfect.

So blanks are: △ and □

Wait — but pos3 is shown as △, which fits. So yes.

Actually, let me write it out:

Pattern: [□][△][△][□] repeated.

Given:
1: □
2: _ → should be △
3: △ → correct
4: _ → should be □
5: □ → starts next group
6: △
7: △
8: □ → ends second group.

Perfect.

✔ Row 1 blanks: △ , □

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Row 2:
△ ⬠ ⬠ _ _ ⬠ ⬠ △

We see:
1: △
2: ⬠
3: ⬠
4: _
5: _
6: ⬠
7: ⬠
8: △

Looks symmetric? Or repeating?

Notice: starts with △, then two ⬠, then two blanks, then two ⬠, then △.

Maybe the pattern is: △ ⬠ ⬠ ⬠ ⬠ △ ? But that’s 6 items.

Wait — total 8 positions.

What if pattern is: △ ⬠ | ⬠ ⬠ △ — but that’s not symmetric.

Another idea: maybe it's palindromic? Read same forwards and backwards.

Forward: △ ⬠ ⬠ _ _ ⬠ ⬠ △

Backward: △ ⬠ ⬠ _ _ ⬠ ⬠ △ — same structure.

So if it’s palindrome, then pos4 must equal pos5? No — pos4 should mirror pos5? Let’s index:

Pos1 ↔ Pos8: both △ — good
Pos2 ↔ Pos7: both ⬠ — good
Pos3 ↔ Pos6: both ⬠ — good
Pos4 ↔ Pos5: they should be equal to each other? In palindrome, pos4 mirrors pos5? Actually, in 8-element list:

Pos1 ↔ Pos8
Pos2 ↔ Pos7
Pos3 ↔ Pos6
Pos4 ↔ Pos5

So pos4 and pos5 should be the same shape.

What shape? Looking at surrounding: after two ⬠, before two ⬠ — maybe another ⬠? But then it would be all ⬠ except ends.

Try: △ ⬠ ⬠ ⬠ ⬠ ⬠ ⬠ △ — but that’s 8 items? 1+6+1=8 — yes.

But in the given, pos6 and pos7 are ⬠, pos8 is △ — so if pos4 and pos5 are ⬠, then:

△ ⬠ ⬠ ⬠ ⬠ ⬠ △ — that works.

And it’s symmetric.

Is there any reason to think otherwise? The problem says “complete the patterns” — symmetry is a valid pattern.

Alternatively, maybe repeating unit of 4: △ ⬠ ⬠ ⬠ | ⬠ ⬠ △ — but last part doesn’t match first.

No, symmetry makes sense.

So blanks: pos4 and pos5 → both ⬠

✔ Row 2 blanks: ⬠ , ⬠

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Row 3:
□ □ _ _ □ □ ○ □

Given:
1: □
2: □
3: _
4: _
5: □
6: □
7: ○
8: □

Look at end: □ □ ○ □ — that’s interesting.

Start: □ □ _ _

Maybe pattern is groups of 4?

First 4: □ □ ? ?
Next 4: □ □ ○ □

Not obviously repeating.

Another idea: perhaps the pattern is based on position or counting.

Notice that ○ appears only once, at pos7.

Maybe the pattern is: two □, then something, then two □, then ○, then □.

But we have two blanks at 3 and 4.

What if the pattern is: □ □ △ △ | □ □ ○ □ — but why △?

Wait — look at the last four: □ □ ○ □ — that might be a clue.

Perhaps the pattern is shifting or changing.

Another approach: count how many of each.

But let’s try to see if there’s a cycle.

Suppose the pattern repeats every 4: but pos1-4 vs pos5-8:

Pos1-4: □ □ _ _
Pos5-8: □ □ ○ □

So if same pattern, then pos3 should be ○, pos4 should be □? But then pos3=○, pos4=□, and pos7=○, pos8=□ — but pos5=□, pos6=□ — so not matching.

Unless the pattern is different.

Wait — what if the pattern is: □ □ X Y, and then □ □ Z W, and we need to find X,Y such that it relates to Z,W.

Z=○, W=□.

But what is the relation?

Perhaps it’s a sequence where the third element changes.

Another idea: maybe it’s □ □ followed by two shapes that are "fillers", then repeats.

But let’s look at the whole thing: □ □ _ _ □ □ ○ □

Notice that after the first two □, we have two blanks, then two □, then ○, then □.

The ○ is at position 7, which is unusual.

Perhaps the pattern is based on the number of sides or something, but that might be overcomplicating.

Let’s consider that the pattern might be: repeat "□ □" but with an insertion.

Or perhaps it's: □ □ △ △ □ □ ○ □ — but why those?

Wait — look at row 4 for comparison, but let's stick to this.

Another thought: maybe the two blanks are meant to be the same as the last two non-blank before them or something.

Before blanks: pos1-2: □ □

After blanks: pos5-6: □ □, then pos7: ○, pos8: □

So perhaps the blanks are ○ and □? Then it would be:

□ □ ○ □ □ □ ○ □ — but then pos3=○, pos4=□, pos5=□, pos6=□, pos7=○, pos8=□ — not very patterned.

Perhaps it's a mirror: pos1=□, pos8=□; pos2=□, pos7=○ — not same; pos3=?, pos6=□; pos4=?, pos5=□.

If palindrome, pos3 should equal pos6=□, pos4 should equal pos5=□.

So blanks: □ and □

Then the row becomes: □ □ □ □ □ □ ○ □

But pos7 is ○, which breaks the □ streak, but it's given.

Is that acceptable? The pattern could be mostly □ with an ○ at pos7.

But why would pos7 be ○? Maybe it's intentional.

Perhaps the pattern is six □ and then ○ □, but we have only 8 positions.

Let's count the □: currently pos1,2,5,6,8 are □ — that's 5, plus two blanks, and pos7 is ○.

If blanks are both □, then 7 □ and one ○ — possible.

But is there a better pattern?

Another idea: perhaps the pattern is "□ □" repeated, but with the third item in each group being different.

Group1: pos1-3: □ □ ?
Group2: pos4-6: ? □ □
Group3: pos7-8: ○ □ — incomplete.

Not working.

Let's look at the answer choices logically. Perhaps the pattern is that the shape at position n is related to n mod something.

But for a student, simpler is better.

Notice that in many rows, the pattern repeats every 4 or is symmetric.

For this row, let's assume it's similar to row 2 — symmetric.

Pos1 and pos8: both □ — good
Pos2 and pos7: pos2=□, pos7=○ — not same, so not symmetric.

Pos3 and pos6: pos6=□, so pos3 should be □ if symmetric
Pos4 and pos5: pos5=□, so pos4 should be □

So again, blanks: □ and □

And the row is: □ □ □ □ □ □ ○ □

It's not perfectly symmetric, but pos7 is ○, which is given, so we have to accept it.

Perhaps the pattern is that every 7th position is ○, but that's arbitrary.

I think for consistency, and since other rows use symmetry or repetition, I'll go with blanks being □ and □.

But let's double-check with another approach.

Suppose the pattern is: the first four are "□ □ A B", and the last four are "□ □ C D", and we know C=○, D=□, and perhaps A and B are the same as C and D or something.

But no direct link.

Perhaps it's a sequence where the third shape is changing: in some rows it's triangle, etc.

Another idea: look at the entire worksheet — perhaps the patterns are designed to be simple repetitions.

Let's skip and come back.

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Row 4:
☆ ☆ △ ☆ _ ☆ _ ☆

Given:
1: ☆
2: ☆
3: △
4: ☆
5: _
6: ☆
7: _
8: ☆

Look at positions: 1,2,4,6,8 are ☆ — that's five stars.

Pos3 is △.

Blanks at 5 and 7.

If the pattern is mostly ☆ with △ at certain positions.

Pos3 is △, so perhaps pos5 or pos7 should be △.

But which one?

Notice that pos3 is △, and it's between two ☆ (pos2 and pos4).

Similarly, if we put △ at pos5, then it's between pos4=☆ and pos6=☆ — good.

Then pos7 is blank, and pos8=☆, pos6=☆, so if pos7=☆, then it's all ☆ except pos3 and pos5 are △.

But let's see the sequence: ☆ ☆ △ ☆ △ ☆ _ ☆

If pos7=☆, then: ☆ ☆ △ ☆ △ ☆ ☆ ☆

Is there a pattern? Positions of △: 3 and 5 — difference of 2.

Next would be 7, but if we put △ at 7, then it's ☆ ☆ △ ☆ △ ☆ △ ☆ — which is alternating after pos2, but pos1 and 2 are both ☆.

From pos3 onwards: △ ☆ △ ☆ △ ☆ — that would be alternating starting with △.

Pos3=△, pos4=☆, pos5=△, pos6=☆, pos7=△, pos8=☆ — perfect alternating.

But in the given, pos4=☆, pos6=☆, pos8=☆ — good.

Pos3=△ — good.

So if we set pos5=△, pos7=△, then from pos3 to pos8: △ ☆ △ ☆ △ ☆ — alternating.

And pos1 and 2 are extra ☆ ☆.

So the pattern could be: two ☆, then alternating △ ☆ starting with △.

Yes, that makes sense.

So blanks: pos5=△, pos7=△

✔ Row 4 blanks: △ , △

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Back to Row 3: □ □ _ _ □ □ ○ □

Now that we've seen other rows, perhaps it's similar.

Given that pos7 is ○, which is different, and others are □.

Perhaps the pattern is that the seventh position is always a different shape, but in other rows, not necessarily.

In row 1, pos7 is △, which is part of the pattern.

Another idea for row 3: perhaps it's "□ □" repeated, but the third pair has a variation.

Or maybe the blanks are ○ and □, to match the end.

Let's try: if blanks are ○ and □, then:

□ □ ○ □ □ □ ○ □

Now, compare to the end: pos5-8: □ □ ○ □

Pos1-4: □ □ ○ □ — same as pos5-8!

Oh! I missed that.

Pos1-4: □ □ ○ □
Pos5-8: □ □ ○ □

Exactly the same!

But in the given, pos3 and pos4 are blank, and pos7 is ○, pos8 is □.

So if pos3=○, pos4=□, then pos1-4: □ □ ○ □

Pos5-8: □ □ ○ □ — given pos5=□, pos6=□, pos7=○, pos8=□ — yes!

Perfect match.

So the pattern is simply repeating "□ □ ○ □" twice.

Therefore, blanks are: ○ , □

✔ Row 3 blanks: ○ , □

I overcomplicated it earlier. Simple repetition.

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Row 5:
○ ⬡ _ ○ _ ⬡ ⬡ ○

Given:
1: ○
2: ⬡
3: _
4: ○
5: _
6: ⬡
7: ⬡
8: ○

Look for pattern.

Notice pos1=○, pos4=○, pos8=○ — so perhaps every 3rd or something.

Pos2=⬡, pos6=⬡, pos7=⬡ — not clear.

Try grouping: perhaps groups of 3 or 4.

Assume repeating every 4: pos1-4: ○ ⬡ ? ○
Pos5-8: ? ⬡ ⬡ ○

Not obvious.

Symmetry? Pos1 and pos8: both ○ — good
Pos2 and pos7: pos2=⬡, pos7=⬡ — good
Pos3 and pos6: pos6=⬡, so pos3 should be ⬡
Pos4 and pos5: pos4=○, so pos5 should be ○

So blanks: pos3=⬡, pos5=○

Then the row: ○ ⬡ ⬡ ○ ○ ⬡ ⬡ ○

Check: pos1-4: ○ ⬡ ○
Pos5-8: ○ ⬡ ⬡ ○ — same!

Perfect repetition of "○ ⬡ ⬡ ○"

Yes!

✔ Row 5 blanks: ⬡ , ○

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Row 6:
⬠ ⬠ _ ⬠ _ ⬠ △ ⬠

Given:
1: ⬠
2: ⬠
3: _
4: ⬠
5: _
6: ⬠
7: △
8: ⬠

Look for pattern.

Pos7 is △, different.

Others are mostly ⬠.

Try symmetry: pos1 and pos8: both ⬠ — good
Pos2 and pos7: pos2=⬠, pos7=△ — not same, so not symmetric.

Repetition: suppose groups of 4.

Pos1-4: ⬠ ⬠ ? ⬠
Pos5-8: ? ⬠ △

Not clear.

Notice that pos7 is △, similar to row 3 where pos7 was ○.

In row 3, we had repetition of 4-shape group.

Here, perhaps "⬠ △ ⬠" or something.

Assume the pattern is "⬠ ⬠ X ⬠" repeated, but pos5-8 is Y ⬠ △ ⬠

If X is △, then pos1-4: ⬠ △ ⬠
Then pos5-8 should be same: ⬠ △ ⬠

But given pos5=_, pos6=⬠, pos7=△, pos8=⬠ — so if pos5=⬠, then it matches: ⬠ △ ⬠

And pos3 should be △ to match.

So blanks: pos3=△, pos5=⬠

Then row: ⬠ ⬠ △ ⬠ ⬠ △ ⬠

Pos1-4: ⬠ ⬠ △ ⬠
Pos5-8: ⬠ ⬠ △ ⬠ — yes, identical.

Perfect.

✔ Row 6 blanks: △ , ⬠

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Row 7:
△ △ _ △ _ △ ⬠ △

Given:
1: △
2: △
3: _
4: △
5: _
6: △
7: ⬠
8: △

Similar to previous.

Pos7 is ⬠, different.

Assume repetition of 4-shape group.

Suppose pattern is "△ △ X △"

Then pos1-4: △ △ ? △
Pos5-8: ? △ ⬠ △

If the group is "△ △ ⬠ △", then pos1-4 should be that, so pos3=⬠

Pos5-8 should be same: △ △ ⬠ △

Given pos5=_, pos6=△, pos7=⬠, pos8=△ — so if pos5=△, then it matches: △ △ ⬠ △

Yes.

So blanks: pos3=⬠, pos5=△

Row: △ △ ⬠ △ △ △ ⬠ △

Pos1-4: △ △ ⬠ △
Pos5-8: △ △ ⬠ △ — good.

✔ Row 7 blanks: ⬠ , △

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Row 8:
⬠ ⬡ ⬡ ⬠ _ ⬡ _

Given:
1: ⬠
2: ⬡
3: ⬡
4: ⬠
5: ⬠
6: _
7: ⬡
8: _

Look for pattern.

Notice pos1=⬠, pos4=⬠, pos5=⬠ — several pentagons.

Pos2=⬡, pos3=⬡, pos7=⬡ — hexagons.

Blanks at 6 and 8.

Try symmetry: pos1 and pos8: pos1=⬠, pos8=_ — if symmetric, pos8 should be ⬠? But let's see.

Pos2 and pos7: both ⬡ — good
Pos3 and pos6: pos3=⬡, so pos6 should be ⬡
Pos4 and pos5: both ⬠ — good, and they are adjacent.

In 8 positions, pos4 and pos5 are middle.

If symmetric, pos6 should mirror pos3=⬡, pos8 should mirror pos1=⬠

So blanks: pos6=⬡, pos8=⬠

Then row: ⬠ ⬡ ⬠ ⬠ ⬡ ⬠

Check: pos1-4: ⬠ ⬡ ⬡ ⬠
Pos5-8: ⬠ ⬡ ⬠ — same!

Perfect repetition.

✔ Row 8 blanks: ⬡ ,

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Now, summarize all answers:

Row 1: △ , □
Row 2: ⬠ ,
Row 3: ○ , □
Row 4: △ , △
Row 5: ⬡ , ○
Row 6: △ , ⬠
Row 7: ⬠ , △
Row 8: ⬡ , ⬠

In the problem, it says "fill in the 2 empty spot" for each row, so we provide the two shapes for each row in order.

Final Answer:

Row 1: triangle, square
Row 2: pentagon, pentagon
Row 3: circle, square
Row 4: star, star
Row 5: hexagon, circle
Row 6: triangle, pentagon
Row 7: pentagon, triangle
Row 8: hexagon, pentagon

But to match the format, probably list the shapes as they appear.

Since the question asks to fill in the blanks, and there are two per row, we can list them in order.

In the response, we should provide the answers clearly.

Final Answer:
For each row, the two missing shapes in order are:
1. triangle, square
2. pentagon, pentagon
3. circle, square
4. star, star
5. hexagon, circle
6. triangle, pentagon
7. pentagon, triangle
8. hexagon, pentagon