Math worksheet for identifying parallel, perpendicular, and intersecting lines using a diagram with labeled lines and angles.

Let’s go step by step to identify each pair of lines as parallel, perpendicular, or intersecting.

First, remember:
- Parallel lines never meet — they run in the same direction and stay the same distance apart.
- Perpendicular lines cross at a right angle (90°) — look for the little square symbol (□) that means “right angle”.
- Intersecting lines cross each other at any angle (not necessarily 90°). If they’re not parallel and not perpendicular, they’re just intersecting.

Now let’s analyze each pair using the diagram:

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1) Line RT and Line VK

Both are vertical lines. In the diagram, both have arrows going up and down, and they never meet. Also, note: both are perpendicular to horizontal lines LZ and EC (see the right-angle marks). So if two lines are both perpendicular to the same line, they are parallel to each other.

→ Parallel

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2) Line SX and Line JP

Line SX is diagonal (going from top-left to bottom-right).
Line JP is vertical.
They cross each other — you can see they meet at one point. The angle isn’t marked as 90°, so it’s not perpendicular. They’re not running in the same direction → not parallel.

→ Intersecting

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3) Line RT and Line JP

Both are vertical lines. Same as #1 — they never meet, both perpendicular to horizontals.

→ Parallel

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4) Line VK and Line SX

VK is vertical. SX is diagonal. They cross at point X (you can see the arrowhead of SX ends near VK, but actually, looking closely — wait! In the diagram, line SX goes through point where VK meets EC? Let me check again.

Actually, looking at the diagram:
Line SX starts at S (top left), goes diagonally down to X (bottom right).
Line VK is vertical, going from V (top) to K (bottom).
At point X, line SX crosses line EC, and also crosses line VK? Wait — no. Point X is on line EC and on line SX. But line VK also passes through that same point? Look: there’s a right-angle mark at the intersection of VK and EC — and SX also goes through that exact spot? Actually, yes — in the diagram, line SX intersects line VK at the point where VK meets EC (point X). And since VK is vertical and SX is diagonal, they form an angle that is NOT 90° (no square symbol there).

So they cross → intersecting. Not perpendicular because no right angle shown.

→ Intersecting

Wait — hold on! Let me double-check #4.

Looking again: At point X, line SX crosses line EC (horizontal) and line VK (vertical). There IS a right-angle symbol between VK and EC — meaning VK ⊥ EC. But what about SX and VK? Is there a right angle between them? No — the right angle is between VK and EC, not between VK and SX. So SX and VK cross at an acute/obtuse angle → still intersecting.

Yes → Intersecting

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5) Line RT and Line SX

RT is vertical. SX is diagonal. They cross somewhere in the middle (between L-Z and E-C). No right angle symbol → not perpendicular. Not same direction → not parallel.

→ Intersecting

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6) Line LZ and Line SX

LZ is horizontal (left-right). SX is diagonal. They cross — you can see SX cuts across LZ. Angle is not 90° (no square symbol at their intersection).

→ Intersecting

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7) Line LZ and Line RT

LZ is horizontal. RT is vertical. Where they meet (at point R/L area?), there’s a right-angle symbol (□). That means they are perpendicular.

→ Perpendicular

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8) Line VK and Line JP

Both are vertical lines. Never meet. Both perpendicular to horizontals.

→ Parallel

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9) Line LZ and Line VK

LZ is horizontal. VK is vertical. At their intersection (point V/Z area?), there’s a right-angle symbol (□). So they are perpendicular.

→ Perpendicular

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10) Line LZ and Line JP

LZ is horizontal. JP is vertical. At their intersection (point J/P area?), there’s a right-angle symbol (□). So they are perpendicular.

→ Perpendicular

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Let me quickly verify all answers against the diagram logic:

Vertical lines: RT, JP, VK → all parallel to each other.
Horizontal lines: LZ, EC → parallel to each other.
Diagonal: