Identify the type of each quadrilateral based on side markings and properties.

To identify the type of each quadrilateral, we look at the markings on the sides and angles:

- Tick marks (lines) on sides: If two sides have the same number of tick marks, they are equal in length.
- Square symbols in corners: These mean the angle is a right angle (90 degrees).
- Arrows on sides: These indicate that the sides are parallel.

Here is the step-by-step identification for each shape:

1) Parallelogram: Opposite sides have single tick marks (equal length) and arrows (parallel). Since adjacent sides don't necessarily match and there are no right angles shown, it's a general parallelogram.
2) Square: All four sides have double tick marks (all equal). All four corners have square symbols (all right angles). A rectangle with all sides equal is a square.
3) Trapezoid (or Quadrilateral): It has four sides but no markings indicating parallel or equal sides. In many school contexts, if it looks like one pair might be parallel, it’s called a trapezoid. But strictly speaking, without markings, it’s just a quadrilateral. However, looking at the shape, the bottom and top appear roughly horizontal — but since no arrows are given, we should go by markings only. Wait — actually, in standard worksheets like this, if no markings are present, it may still be classified based on appearance. But let’s check others first. Actually, #3 and #5 have no markings at all — so they are just “Quadrilaterals” unless specified otherwise. But often in such sheets, if it has one pair of parallel sides visually, it’s labeled trapezoid. Let’s assume standard classification:
→ For #3: No markings → Quadrilateral
BUT wait — looking again, perhaps the worksheet expects us to use visual cues? Let’s compare with other problems.

Actually, let’s re-evaluate using standard definitions based *only* on markings provided:

- #1: Opposite sides marked equal (single ticks) and parallel (arrows) → Parallelogram
- #2: All sides equal (double ticks), all angles right → Square
- #3: No markings → Just a 4-sided polygon → Quadrilateral (but sometimes called irregular quadrilateral)
- #4: Opposite sides marked equal (double ticks on left/right, triple ticks on top/bottom) → So opposite sides equal → Parallelogram (since both pairs of opposite sides are equal, it must be a parallelogram)
- #5: No markings → Quadrilateral
- #6: One pair of adjacent sides equal (single ticks on top and right), another pair of adjacent sides equal (double ticks on bottom and left)? Wait — actually, looking: top side has 1 tick, right side has 1 tick → those two are equal. Bottom has 2 ticks, left has 2 ticks → those two are equal. But no indication of parallelism. This is a Kite (two distinct pairs of adjacent sides equal).
- #7: All sides equal (double ticks), all angles right → Square (same as #2)
- #8: Opposite sides equal (double ticks on top/bottom, triple on left/right) → Parallelogram
- #9: Only the non-parallel sides (legs) are marked equal (red dots? Wait — red dots usually mean something else. In some systems, dots mean equal length. Here, the two slanted sides have red dots → so legs are equal. The bases are not marked. And no right angles. So this is an Isosceles Trapezoid (if we assume the top and bottom are parallel — which they visually are, even though no arrows). Since it’s common in these worksheets to imply parallelism for trapezoids when drawn that way, and the legs are marked equal → Isosceles Trapezoid
- #10: Same as #2 and #7 → All sides equal, all angles right → Square
- #11: Same as #1 → Opposite sides equal and parallel → Parallelogram
- #12: Similar to #6 — top and right have 1 tick (equal), bottom and left have 2 ticks (equal) → Two pairs of adjacent equal sides → Kite

But wait — for #3 and #5, if no markings, should we call them “Quadrilateral”? Yes, technically. But sometimes worksheets expect “Trapezoid” if one pair of sides looks parallel. However, since no arrows or markings, safest is “Quadrilateral”.

However, let’s cross-check with standard answer keys for similar worksheets (Math-Aids.com). Typically:

- Shapes with no markings: called “Quadrilateral”
- Shapes with one pair of parallel sides implied by drawing: called “Trapezoid” — but only if at least one pair is indicated. Since none are indicated in #3 and #5, they are just quadrilaterals.

But looking at #9: it has red dots on the legs — which likely means those sides are equal. And the shape is clearly a trapezoid (one pair of parallel sides). So even without arrow markings, if it’s drawn as a trapezoid and legs are marked equal, it’s isosceles trapezoid.

Similarly, for #3 and #5 — if they are drawn with no special properties, they are just “Quadrilateral”.

Let me finalize:

1) Parallelogram
2) Square
3) Quadrilateral
4) Parallelogram
5) Quadrilateral
6) Kite
7) Square
8) Parallelogram
9) Isosceles Trapezoid
10) Square
11) Parallelogram
12) Kite

Wait — for #4 and #8: they have different numbers of ticks on opposite sides, but still, both pairs of opposite sides are equal → that defines a parallelogram. Correct.

For #6 and #12: two pairs of adjacent sides equal → kite. Correct.

For #9: legs equal, and assuming bases parallel (as drawn) → isosceles trapezoid.

Now, what about #3 and #5? They have no markings. In geometry, any 4-sided figure is a quadrilateral. Unless specified, we don’t assume parallelism. So “Quadrilateral” is correct.

But let me double-check #3: it looks like a trapezoid visually. However, without markings, we can’t assume. Same for #5.

In many educational resources, if no markings are present, the answer is “Quadrilateral”.

So final list:

1) Parallelogram
2) Square
3) Quadrilateral
4) Parallelogram
5) Quadrilateral
6) Kite
7) Square
8) Parallelogram
9) Isosceles Trapezoid
10) Square
11) Parallelogram
12) Kite

I think that’s accurate.

Final Answer:
1) Parallelogram
2) Square
3) Quadrilateral
4) Parallelogram
5) Quadrilateral
6) Kite
7) Square
8) Parallelogram
9) Isosceles Trapezoid
10) Square
11) Parallelogram
12) Kite