Parallel, Perpendicular and intersecting lines worksheet | Live ... - Free Printable
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Step-by-step solution for: Parallel, Perpendicular and intersecting lines worksheet | Live ...
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Show Answer Key & Explanations
Step-by-step solution for: Parallel, Perpendicular and intersecting lines worksheet | Live ...
Let's analyze the diagram and determine the relationship between each pair of lines: parallel, perpendicular, or intersecting.
We are given a geometric figure with several labeled points and lines. The diagram includes:
- Rectangle JKBH (or possibly JKBC), but more clearly, JK and CD appear to be horizontal.
- Rectangle BCDE and EFDG form a larger rectangle-like structure.
- A diagonal line from A through I, H, and G, forming triangle AGF.
- Several right angles (marked with blue squares) at points: J, K, C, D, B, E, F, indicating perpendicularity.
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1. Line HE and line GF
- HE is a vertical segment from H to E.
- GF is a horizontal segment from G to F.
- They meet at point E, and since HE is vertical and GF is horizontal, they form a right angle.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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2. Line BI and line BA
- BI is part of the diagonal line from B to I.
- BA is the vertical line from B to A.
- These two lines meet at point B.
- Since BI is slanted and BA is vertical, they are not parallel.
- They cross at an angle that is not 90° (not marked as right angle), so they are intersecting but not perpendicular.
- ✔ Intersecting
> ✔️ Answer: Intersecting
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3. Line GA and line KD
- GA is the diagonal from G to A (passes through H and I).
- KD is the horizontal line from K to D.
- KD goes from left to right across the bottom of the figure.
- GA crosses KD at point H.
- So they intersect at H.
- Not parallel (different directions), not necessarily at 90° (no right angle mark).
- ✔ Intersecting
> ✔️ Answer: Intersecting
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4. Line FA and line JC
- FA is vertical (from F to A).
- JC is horizontal (from J to C).
- These two lines do not appear to touch in the diagram.
- But we can check if they are parallel, perpendicular, or intersecting.
- FA is vertical; JC is horizontal → if extended, they would meet at some point.
- However, FA and JC are not the same line, and they are not parallel.
- But they do not intersect in the diagram — but are they perpendicular?
- Yes — vertical and horizontal lines are perpendicular even if they don’t intersect in the diagram, as long as their directions are perpendicular.
- Wait: Are they actually perpendicular?
- FA is vertical.
- JC is horizontal.
- So they are perpendicular because one is vertical and one is horizontal.
- Even if they don’t intersect in the drawing, their directions make them perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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5. Line BE and line CD
- BE is vertical (from B to E).
- CD is horizontal (from C to D).
- BE and CD are adjacent sides of a rectangle (BCDE).
- They meet at point E.
- Right angle is marked at E → so they are perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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6. Line KE and line GF
- KE is horizontal (from K to E).
- GF is horizontal (from G to F).
- Both are horizontal lines.
- Are they the same line? No.
- But they are both horizontal → parallel.
- Do they intersect? No — they are on different levels.
- ✔ Parallel
> ✔️ Answer: Parallel
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7. Line CI and line AF
- CI is horizontal (from C to I).
- AF is vertical (from A to F).
- CI is part of the top side of rectangle BCDE.
- AF is the vertical line from A down to F.
- These lines intersect at point I (since I is on CI and AF).
- At point I, CI is horizontal, AF is vertical → forms a right angle.
- Right angle is not explicitly marked, but based on geometry:
- AF is vertical (as seen from A to F passing through B and E).
- CI is horizontal (same level as JC).
- So they are perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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8. Line BJ and line HA
- BJ is horizontal (from B to J).
- HA is part of the diagonal from H to A.
- BJ is horizontal.
- HA is a diagonal line from H to A (part of GA).
- They intersect at point I? Wait — let’s check:
- BJ: from B to J → this is the top horizontal line from B to J.
- HA: from H to A → this is the diagonal from lower-left to upper-right.
- They meet at point I, which lies on both BJ and HA.
- So they intersect at I.
- Is it a right angle? No marking → not necessarily perpendicular.
- Directions: BJ is horizontal, HA is diagonal → not vertical.
- So not perpendicular.
- Therefore, they are intersecting.
- ✔ Intersecting
> ✔️ Answer: Intersecting
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| # | Pair of Lines | Relationship |
|---|-------------------------------|--------------------|
| 1 | Line HE and line GF | Perpendicular |
| 2 | Line BI and line BA | Intersecting |
| 3 | Line GA and line KD | Intersecting |
| 4 | Line FA and line JC | Perpendicular |
| 5 | Line BE and line CD | Perpendicular |
| 6 | Line KE and line GF | Parallel |
| 7 | Line CI and line AF | Perpendicular |
| 8 | Line BJ and line HA | Intersecting |
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✔ Completed! Let me know if you'd like a visual explanation or how to identify these relationships in general.
We are given a geometric figure with several labeled points and lines. The diagram includes:
- Rectangle JKBH (or possibly JKBC), but more clearly, JK and CD appear to be horizontal.
- Rectangle BCDE and EFDG form a larger rectangle-like structure.
- A diagonal line from A through I, H, and G, forming triangle AGF.
- Several right angles (marked with blue squares) at points: J, K, C, D, B, E, F, indicating perpendicularity.
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Step-by-step analysis:
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1. Line HE and line GF
- HE is a vertical segment from H to E.
- GF is a horizontal segment from G to F.
- They meet at point E, and since HE is vertical and GF is horizontal, they form a right angle.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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2. Line BI and line BA
- BI is part of the diagonal line from B to I.
- BA is the vertical line from B to A.
- These two lines meet at point B.
- Since BI is slanted and BA is vertical, they are not parallel.
- They cross at an angle that is not 90° (not marked as right angle), so they are intersecting but not perpendicular.
- ✔ Intersecting
> ✔️ Answer: Intersecting
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3. Line GA and line KD
- GA is the diagonal from G to A (passes through H and I).
- KD is the horizontal line from K to D.
- KD goes from left to right across the bottom of the figure.
- GA crosses KD at point H.
- So they intersect at H.
- Not parallel (different directions), not necessarily at 90° (no right angle mark).
- ✔ Intersecting
> ✔️ Answer: Intersecting
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4. Line FA and line JC
- FA is vertical (from F to A).
- JC is horizontal (from J to C).
- These two lines do not appear to touch in the diagram.
- But we can check if they are parallel, perpendicular, or intersecting.
- FA is vertical; JC is horizontal → if extended, they would meet at some point.
- However, FA and JC are not the same line, and they are not parallel.
- But they do not intersect in the diagram — but are they perpendicular?
- Yes — vertical and horizontal lines are perpendicular even if they don’t intersect in the diagram, as long as their directions are perpendicular.
- Wait: Are they actually perpendicular?
- FA is vertical.
- JC is horizontal.
- So they are perpendicular because one is vertical and one is horizontal.
- Even if they don’t intersect in the drawing, their directions make them perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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5. Line BE and line CD
- BE is vertical (from B to E).
- CD is horizontal (from C to D).
- BE and CD are adjacent sides of a rectangle (BCDE).
- They meet at point E.
- Right angle is marked at E → so they are perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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6. Line KE and line GF
- KE is horizontal (from K to E).
- GF is horizontal (from G to F).
- Both are horizontal lines.
- Are they the same line? No.
- But they are both horizontal → parallel.
- Do they intersect? No — they are on different levels.
- ✔ Parallel
> ✔️ Answer: Parallel
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7. Line CI and line AF
- CI is horizontal (from C to I).
- AF is vertical (from A to F).
- CI is part of the top side of rectangle BCDE.
- AF is the vertical line from A down to F.
- These lines intersect at point I (since I is on CI and AF).
- At point I, CI is horizontal, AF is vertical → forms a right angle.
- Right angle is not explicitly marked, but based on geometry:
- AF is vertical (as seen from A to F passing through B and E).
- CI is horizontal (same level as JC).
- So they are perpendicular.
- ✔ Perpendicular
> ✔️ Answer: Perpendicular
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8. Line BJ and line HA
- BJ is horizontal (from B to J).
- HA is part of the diagonal from H to A.
- BJ is horizontal.
- HA is a diagonal line from H to A (part of GA).
- They intersect at point I? Wait — let’s check:
- BJ: from B to J → this is the top horizontal line from B to J.
- HA: from H to A → this is the diagonal from lower-left to upper-right.
- They meet at point I, which lies on both BJ and HA.
- So they intersect at I.
- Is it a right angle? No marking → not necessarily perpendicular.
- Directions: BJ is horizontal, HA is diagonal → not vertical.
- So not perpendicular.
- Therefore, they are intersecting.
- ✔ Intersecting
> ✔️ Answer: Intersecting
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Final Answers:
| # | Pair of Lines | Relationship |
|---|-------------------------------|--------------------|
| 1 | Line HE and line GF | Perpendicular |
| 2 | Line BI and line BA | Intersecting |
| 3 | Line GA and line KD | Intersecting |
| 4 | Line FA and line JC | Perpendicular |
| 5 | Line BE and line CD | Perpendicular |
| 6 | Line KE and line GF | Parallel |
| 7 | Line CI and line AF | Perpendicular |
| 8 | Line BJ and line HA | Intersecting |
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✔ Completed! Let me know if you'd like a visual explanation or how to identify these relationships in general.
Parent Tip: Review the logic above to help your child master the concept of parallel intersecting and perpendicular lines worksheet.
