G1a - 2D geometry - terms and notation - BossMaths.com - Free Printable

Let’s go step by step.

We are looking at a quadrilateral (4-sided shape) labeled ABCD.

From the markings:

- Sides AB and DC each have one tick mark → that means they are equal in length.
- Sides AD and BC each have one arrowhead → that means they are parallel to each other.
- Angles at B and C each have two curved lines → that means angle B = angle C.
- Angles at A and D each have one curved line → that means angle A = angle D.
- Also, since AD ∥ BC, and AB and DC are the non-parallel sides (but equal), this is an isosceles trapezoid.

Now let’s answer each part:

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(a) Which two edges are of equal length?

Look for matching tick marks.
AB has one tick.
DC has one tick.
→ So AB and DC are equal.

Also, note: AD and BC are marked with arrows — those mean *parallel*, not necessarily equal. In fact, in a trapezoid, the two bases (AD and BC) are usually different lengths unless it’s a rectangle or parallelogram — but here, only one pair of sides is parallel (wait — actually, both pairs? Let’s check part d).

Wait — hold on! The diagram shows:

- AD has an arrow pointing right.
- BC has an arrow pointing right → so AD ∥ BC.
- But what about AB and DC? They don’t have arrows — so we can’t assume they’re parallel.

BUT — in the diagram, AB and DC have tick marks meaning they are equal in length — and angles at base are equal — so yes, this is an isosceles trapezoid with only one pair of parallel sides: AD and BC.

So back to (a): Edges with same marking → AB and DC.

✔ Answer for (a): AB and DC

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(b) Write down a pair of equal angles.

Angles with same number of arcs are equal.

Angle B and Angle C both have two arcs → so ∠B = C.

Also, Angle A and Angle D both have one arc → so ∠A = ∠D.

Either pair is correct.

✔ We’ll pick: ∠B and ∠C

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(c) Write down a pair of different angles.

We need two angles that are NOT equal.

For example: ∠A and ∠B.

∠A has one arc, ∠B has two arcs → so they are different.

Also, in a trapezoid with AD ∥ BC, consecutive angles between the parallel sides are supplementary (add to 180°), but not necessarily equal — unless it’s a rectangle.

Here, since it’s isosceles, ∠A = D, and ∠B = ∠C, but ∠A ≠ ∠B (unless it’s a rectangle, which it isn’t — because if all angles were equal, it would be a rectangle, but then opposite sides would be equal AND parallel — here, only one pair of sides is marked parallel? Wait — let’s double-check.)

Actually — look again:

The diagram shows:

- AD has an arrow → direction right
- BC has an arrow → direction right → so AD ∥ BC
- AB and DC have NO arrows → so we cannot assume they are parallel.

Therefore, only ONE pair of parallel sides → trapezoid.

And since legs AB and DC are equal (tick marks), and base angles equal → isosceles trapezoid.

In such a shape, adjacent angles along the leg are supplementary, but not equal.

So ∠A + ∠B = 180°, but ∠A ≠ ∠B (unless 90° each — but no indication of that).

So any angle from top vs bottom will be different.

Example: ∠A and B → different.

Or ∠A and ∠C → also different.

✔ Pick: ∠A and ∠B

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(d) True or false: this shape has two pairs of parallel sides.

We already saw:

- AD ∥ BC (both have arrows)
- What about AB and DC? No arrows → so not marked as parallel.

In fact, in an isosceles trapezoid, only one pair of sides is parallel.

If it had two pairs, it would be a parallelogram — and in a parallelogram, opposite sides are equal AND parallel.

Here, AB = DC (equal), but are they parallel? Not indicated. And visually, they sl inward — so likely not parallel.

Moreover, if AB were parallel to DC, and AD parallel to BC, then it would be a parallelogram — and in a parallelogram, opposite angles are equal, and consecutive angles sum to 180°.

But here, we have ∠A = D and ∠B = ∠C — which is consistent with isosceles trapezoid, not general parallelogram.

In a parallelogram, ∠A should equal ∠C, and ∠B equal ∠D — but here, ∠A = ∠D, ∠B = C — so unless it’s a rectangle, it doesn’t fit.

Since no right angles are marked, and sides aren’t all equal, it’s not a rectangle.

Thus, only one pair of parallel sides.

✔ So statement is FALSE.

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Final Answers:

(a) AB and DC
(b) ∠B and C (or A and ∠D)
(c) ∠A and B (or any top and bottom angle)
(d) False

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Final Answer:
(a) AB and DC
(b) ∠B and C
(c) ∠A and ∠B
(d) False