Without trusting your eyes
Cutting a line exactly in half
A ruler finds a midpoint only as well as you can read its scale.
📚 Chapter Learning Kit
Constructions and Tilings · Class 7 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
⚡ Veda Bites
💡 Key Idea
💡 Key Idea
💡 Key Idea
💡 Key Idea
💡 Key Idea
💡 Key Idea
The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Four arcs and one line
The construction
Open the compass wider than half the segment. Draw an arc above and below from each end.
A fixed distance from one point
What an arc really means
Every point on an arc is the same distance from the compass point.
Without reading a protractor
Halving an angle exactly
A protractor halves 76 degrees only as well as you can read its scale.
One arc, then two more
The construction
From the corner, draw an arc crossing both arms, and mark the two crossings.
And the angle is cut in two
Joining to the corner
Call the meeting point P and draw the line from the corner through it.
📖 Smart notes
What you'll study, topic by topic
1
The perpendicular bisector, and why it works
Equal arcs from both ends of a segment cross at two points, and the line through them is the perpendicular bisector. Each crossing is equally far from both ends, which makes the line a mirror for the segment, so it bisec…
- Open the compass wider than half the segment before starting.
- Draw an arc above and below from each end, keeping one opening.
- The line through the two crossings is the perpendicular bisector.
~40 min · full explanation, examples & memory tricks in the app
2
Bisecting and copying an angle
An arc across both arms, then equal arcs from the two crossings, give a point whose line to the corner halves the angle. Two triangles with three pairs of equal sides are congruent by SSS, so the halves are equal. Carryi…
- Draw one arc from the corner across both arms of the angle.
- Draw equal arcs from the two crossings, meeting inside the angle.
- The line from the corner to that meeting point is the bisector.
~40 min · full explanation, examples & memory tricks in the app
3
Tiling: which shapes fill a floor
Tiling covers a surface with no gaps and no overlaps. The angles meeting at every point must total exactly 360 degrees. That one test leaves only three regular shapes: the equilateral triangle, the square and the regular…
- Tiling covers a surface with no gaps left and no overlapping.
- Angles meeting at any point must total exactly 360 degrees.
- A total under 360 leaves a gap, and over 360 means an overlap.
~40 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Why is finding a midpoint with a compass better than with a ruler?
Advanced
A A ruler cannot be used on a segment that is longer than it
B A compass is quicker to use than a ruler for the same job
C The result is easier to label once the arcs have been drawn
D The crossings are exact, while a ruler reading is only close
Show answer & explanation
The crossings are exact, while a ruler reading is only close
A ruler gives the midpoint to the nearest millimetre. The arcs cross where the distances are equal, with no reading involved.
A segment is to be bisected with a compass, and the opening has to be chosen before any arc is drawn. The first step is to open the compass
Beginner
A wider than half the segment
B to exactly half of the segment
C to the whole length of the segment
D as narrow as it will go
Show answer & explanation
wider than half the segment
Or the arcs will not meet.
From each end of the segment you draw arcs numbering
Beginner
A one
B two
C three
D four
Show answer & explanation
two
One above the line and one below.
The two pairs of arcs cross at points numbering
Beginner
A two
B one
C three
D four
Show answer & explanation
two
One above and one below.
🃏 Flashcards
Tap a card to flip it
51 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Memory Match
Categorization
Fact Or Myth
Sequence Builder
Word Match
Playable in the app
Study it properly — free, in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.