Square and rectangle worksheet - Free Printable

Let’s go step by step through each statement using the figure.

We are told:
- AB = 6 cm (top side)
- BD = 3 cm? Wait — actually, looking at the labels:
The vertical sides are labeled “3cm” — that’s AD and BC? But wait, points are A, B, C, D.

Actually, from the diagram:

Points:
- Top left: A
- Top right: B → so AB is top side = 6 cm
- Bottom right: D → so BD is diagonal? No — wait, labeling order matters.

In rectangle ABCD, usually it goes around: A→B→C→D→A.

But in the diagram:
- A is top-left
- B is top-right
- C is bottom-left
- D is bottom-right

So:
- AB = top = 6 cm
- BC = right side? But label says “3cm” next to the right side — which is between B and D? That doesn’t make sense.

Wait — look again: the “3cm” is written on the right side, between B and D? But if D is bottom-right, then the right side should be from B to D? That would mean BD is a side? But then what about C?

Actually, standard labeling for quadrilateral ABCD is clockwise or counter-clockwise.

From the diagram:
- Left side: from A to C → labeled with tick marks (same as bottom side)
- Top side: A to B = 6 cm
- Right side: B to D = 3 cm? But that would make it not a rectangle unless...

Wait — perhaps there's a mislabeling in my assumption.

Looking carefully:

The shape has:
- Top side: A to B = 6 cm
- Right side: B to D = 3 cm → but then D is bottom-right
- Bottom side: C to D = ? (has same tick mark as left side)
- Left side: A to C = ? (has same tick mark as bottom)

Actually, this suggests:
- Opposite sides equal: AB = CD = 6 cm
- AC = BD = 3 cm? But AC is left side, BD is right side? Then yes — both 3 cm.

But then point C is bottom-left, D is bottom-right.

So sides:
- AB = 6 cm (top)
- BD = 3 cm? Wait — no! If D is bottom-right, then the right side is from B to D — so BD is a side? But then the bottom side is from C to D.

That means the four vertices are:
- A (top-left)
- B (top-right)
- D (bottom-right) ← unusual, usually it’s C here
- C (bottom-left)

So the rectangle is labeled A-B-D-C? That’s odd.

But regardless of labeling, we can see:

From the diagram:
- Horizontal sides (top and bottom) are marked with double ticks → they are equal → both 6 cm
- Vertical sides (left and right) are marked with single ticks → they are equal → both 3 cm

Also, diagonals: AC and BD — these connect opposite corners.

Now let’s evaluate each statement:

1. Figure ABCD is a rectangle.
→ It has 4 straight sides, opposite sides equal, all angles 90° (implied by being called square/rectangle section). Also, adjacent sides perpendicular. So YES.

2. Line AB is 3cm long.
→ Diagram shows AB = 6 cm. So NO.

3. Line AC and line BD has equal length.
→ These are diagonals of a rectangle. In any rectangle, diagonals are equal. So YES.

4. Figure ABCD has 4 straight sides.
→ Yes, it’s a quadrilateral. All sides are straight. YES.

5. Line AB is parallel to line CD.
→ AB is top, CD is bottom → in rectangle, opposite sides parallel. YES.

6. Line BD is parallel to line AB.
→ BD is a diagonal (from top-right to bottom-right? Wait — if D is bottom-right, and B is top-right, then BD is vertical? But earlier we said right side is 3 cm — so if B to D is vertical, then BD is a side, not diagonal.

Hold on — I think I made a mistake in vertex labeling.

Let me reassign based on standard convention and diagram clues:

Typically, rectangles are labeled in order: A-B-C-D going around.

In the diagram:
- A is top-left
- B is top-right → so AB is top
- Then next should be C — but in diagram, below B is labeled D? And below A is labeled C?

Actually, looking at the letters placed:

Left side: A (top), C (bottom) → so AC is left side

Right side: B (top), D (bottom) → so BD is right side

Bottom side: C to D

Top side: A to B

So the rectangle is A-B-D-C? That’s not standard, but possible.

Sides:
- AB = 6 cm (top)
- BD = 3 cm (right side) — but BD is from B to D, which is vertical
- DC = ? (bottom) — should be equal to AB = 6 cm
- CA = ? (left) — should be equal to BD = 3 cm

Diagonals:
- From A to D? Or A to C? Wait — diagonal would be A to D and B to C.

But statement 3 says: Line AC and line BD has equal length.

AC is left side (vertical) = 3 cm

BD is right side (vertical) = 3 cm → so they are equal, but they are sides, not diagonals.

But the statement says "line AC and line BD" — in the context, if AC and BD are both vertical sides, then yes, equal.

But typically in rectangle ABCD, diagonals are AD and BC.

This is confusing due to labeling.

Perhaps the intended labeling is:

Vertices:
- A: top-left
- B: top-right
- C: bottom-right
- D: bottom-left

But in the diagram, the bottom-left is labeled C, bottom-right is labeled D.

And the right side is from B to D — which would be diagonal if C is bottom-right.

I think there's a labeling inconsistency in the diagram vs standard.

To resolve, let's use the measurements given:

From diagram:
- Top side AB = 6 cm
- Right side: labeled 3 cm — and it's between B and D, so if D is bottom-right, then BD is a side of length 3 cm
- Bottom side: from C to D — has same tick as left side, so should be 6 cm? But left side is from A to C — which is vertical.

Actually, the tick marks indicate equality:

- Double tick on AB and CD → so AB = CD = 6 cm
- Single tick on AC and BD? Wait, AC is left side, BD is right side — both have single tick? In diagram, left side (A to C) has single tick, right side (B to D) has single tick — so AC = BD = 3 cm

Then diagonals would be AD and BC.

But statement 3 says "Line AC and line BD" — which are the two vertical sides, both 3 cm, so equal. So YES.

Statement 8: Total length of line AB, BD, CD and AC is 18cm.

AB = 6, BD = 3, CD = 6, AC = 3 → sum = 6+3+6+3 = 18 cm → YES.

But are these all sides? AB, BD, CD, AC — that's not the perimeter; it's including two sides and two... wait, AC and BD are sides, AB and CD are sides — so it's all four sides? But in order, it's AB, BD, CD, AC — which is not consecutive, but still the four sides.

Perimeter is AB + BC + CD + DA — but here it's AB, BD, CD, AC.

BD is a side (if D is bottom-right), AC is a side (left), so yes, it's the four sides: AB, BD, CD, AC — but BD and AC are not adjacent in naming, but geometrically, they are the four sides.

Lengths: AB=6, BD=3, CD=6, AC=3 → total 18. Correct.

Now statement 6: Line BD is parallel to line AB.

BD is vertical (right side), AB is horizontal (top) — so they are perpendicular, not parallel. So NO.

Statement 7: Line CD is 6cm long.

CD is bottom side, same as AB (double tick), so 6 cm. YES.

Statement 2: Line AB is 3cm long — no, it's 6 cm. NO.

Statement 1: Is it a rectangle? With opposite sides equal and all angles 90°, yes. Even though labeling is non-standard, the shape is a rectangle. YES.

Statement 4: 4 straight sides — obviously yes. YES.

Statement 5: AB parallel to CD — both horizontal, yes. YES.

Statement 3: AC and BD equal — both 3 cm, yes. YES.

Statement 8: Sum is 18 — calculated above, yes. YES.

Now list:

1. YES
2. NO
3. YES
4. YES
5. YES
6. NO
7. YES
8. YES

Double-check statement 6: BD and AB — BD is vertical, AB is horizontal — not parallel. Correct, NO.

Statement 3: AC and BD — if AC is left side, BD is right side, both vertical, same length — equal. YES.

Even if someone thinks AC and BD are diagonals, in this labeling, they are not — diagonals would be AD and BC.

But the statement says "line AC and line BD", and in the figure, those are the vertical sides.

So all good.

Final Answer:

1. YES
2. NO
3. YES
4. YES
5. YES
6. NO
7. YES
8. YES