Geometry Worksheets - Free Printable

Let’s go step by step to solve each part of the problem.

---

Problem 1:

We are given a diagram with points labeled A, B, C, D, E, and lines/rays/segments drawn between them.

a) Name all the points.
Look at the diagram — every labeled dot is a point.
→ Points: A, B, C, D, E

b) Name any three rays.
A ray starts at one point and goes through another, extending infinitely in one direction. It’s named with two letters: first letter is the endpoint, second is any other point on the ray.
Examples from the diagram:
- Ray starting at D going through E → DE (with arrow over it, but we write as “ray DE”)
- Ray starting at D going through A → DA
- Ray starting at B going through C → BC
(You can pick any three that exist in the diagram.)

c) Name any two line segments.
A line segment has two endpoints and doesn’t extend forever.
Examples:
- Segment AB (between A and B)
- Segment DC (between D and C)

d) Name the line in two ways.
A line extends infinitely in both directions. In the diagram, there’s a straight line passing through D, A, and C.
So you can name it using any two points on it:
- Line DA
- Line AC
(or Line DC, etc.)

---

Problem 2:

Diagram shows intersecting lines with points Q, R, S, T, U, V, W.

a) Name the line that contains the point Q.
Point Q lies on the vertical line that also passes through R and S.
→ That line can be called line RS or line QR or line QS — but since Q is on the line with R and S, best answer: line RS (or specify using Q and another point like QR).

Actually, looking carefully: Q is on the vertical line with R and S. So the line containing Q is the same as line RS. But to include Q, we can say line QR or line QS. Either is fine. Let’s pick line QR.

Wait — actually, in standard naming, if Q is between R and S, then the line is still called line RS. But since the question says “contains point Q”, we can name it using Q and any other point on that line. So:

→ Line QR or Line QS — let’s choose Line QR

But wait — maybe better to use the full line: since R-Q-S are colinear, the line is line RS, and Q is on it. But the question asks to “name the line” — so we can name it using any two points on it. So:

✔ Final choice for (a): Line RS (since it’s the full line, and Q is on it)

But to be precise and include Q, perhaps Line RQ or Line SQ — I think either is acceptable. Let’s go with Line RQ to show Q is included.

Actually, let me re-read: “Name the line that contains the point Q.” So any name for that line is fine. Since R and S are also on it, Line RS is correct. But to make sure Q is mentioned? No — the line is the same regardless. So:

→ Line RS

But let’s check the diagram again mentally: typically in such diagrams, if Q is the intersection point, and R and S are on opposite sides, then line RS contains Q. So yes.

I’ll go with Line RS

b) Name the two opposite rays.
Opposite rays share the same endpoint and go in opposite directions, forming a straight line.

In the diagram, at point Q, we have rays going up to R and down to S — those are opposite rays because they form a straight line and start at Q.

Also, horizontally: from Q to T and Q to V — those are opposite too.

The question says “the two opposite rays” — probably referring to one pair. Let’s pick the vertical ones:

→ Ray QR and Ray QS (they start at Q and go opposite directions)

Or horizontal: Ray QT and Ray QV

Either pair is correct. Let’s pick Ray QR and Ray QS

c) Name the endpoint of QU.
QU is a ray or segment? The notation “QU” usually means a ray starting at Q and going through U, unless specified otherwise. But in context, since it says “endpoint”, it must be a ray or segment.

If it’s ray QU, then endpoint is Q.

If it’s segment QU, endpoints are Q and U — but the question says “the endpoint” (singular), so likely it’s a ray.

Looking at diagram: U is on the diagonal line from Q. So ray QU starts at Q and goes through U.

→ Endpoint is Q

d) Name all the points that lie on the line TV.
Line TV is the horizontal line passing through T, Q, and V.

So points on that line: T, Q, V

Are there others? Probably not — based on typical diagram.

→ Points: T, Q, V

---

Now let’s compile final answers clearly.

Final Answer:

1.
a) A, B, C, D, E
b) Any three rays: e.g., ray DE, ray DA, ray BC
c) Any two line segments: e.g., segment AB, segment DC
d) Line DA and line AC (or any two names for the same line, like line DC and line AD)

2.
a) Line RS (or line RQ or line SQ — any name for the vertical line containing Q)
b) Ray QR and ray QS (or ray QT and ray QV — any pair of opposite rays from Q)
c) Q
d) T, Q, V