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CBSE Class 8 · Mathematics

Quadrilaterals

Official NCERT chapter from Ganita Prakash Part I (book code hegp1). ExamMaster notes are original teaching at CBSE Class 8 depth.

This lesson follows the official chapter “Quadrilaterals” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 8
  • Easy level
  • 8 concepts

1Rectangles and Squares

A rectangle has four right angles; a square is a rectangle with four equal sides. The test is angles and sides, not a “looks boxy” shrug.

A parallelogram that is long and thin is not a rectangle until 90° is tested.

Figure. A rectangle has four right angles; opposite sides are equal. A square is the rectangle whose sides are all equal — here the square is drawn 1:1 in this 1.8:1 frame (width = height / 1.8). The rectangle is drawn 2:1 visually. Right-angle L marks sit in one corner of each.

How it works

  1. Check four right anglesRectangle.
  2. Then check four equal sidesSquare if yes.
  3. Refuse a look-only boxRun the tests.

2Angles in a Quadrilateral

The four interior angles of any simple quadrilateral add to 360°. A split into two triangles (180° + 180°) is the reason at this class. One 90° does not finish the sum.

Adding only the two obvious corners is a half-sum.

Figure. Interior angles of any quadrilateral sum to 360°. This parallelogram is drawn with a true 60° at A and C and 120° at B and D in the 1.8:1 frame: the rise/run of AD is tan 60° after aspect. 60 + 120 + 60 + 120 = 360.

How it works

  1. See four interior anglesThis quad.
  2. Use 360° as the totalOr two triangles.
  3. Find a missing angle as 360° minus the three you knowThe job.

Missing angle

A quadrilateral has angles 80°, 95°, and 110°. What is the fourth?

  • Sum of three285°
  • Fourth360° − 285°
  • Angle75°

Pro tip. Four interiors add to 360°.

3Quadrilaterals with Equal Sidelengths

A rhombus has four equal sides. A square is a rhombus with right angles. Equal sidelengths are the rhombus-test; 90° is extra for the square.

Four equal-looking ticks drawn freehand are not the test until you construct or measure.

Figure. A rhombus is the quadrilateral with all four sides equal. The diagonals here are perpendicular and bisect each other, so each side is 0.33 of the figure height — one length, four times. This is not a square: the diagonals are unequal (0.56 vs 0.36 visually).

How it works

  1. Check four equal sidesRhombus family.
  2. Check right angles if you need a squareThe extra test.
  3. A rhombus that is not a square has equal sides without 90°Two names.

4Playing with Quadrilaterals

Playing here means a property you can change and re-test: move a vertex, ask which name still holds. Play is a test-rerun, not doodling.

A pretty new drawing with no test is decoration.

Figure. Playing with a quadrilateral: shear a rectangle into a parallelogram. Both shapes share base 0.30 of the width and height 0.42 of the height, so the area is unchanged. The slant is a move, not a new area.

How it works

  1. Change one markA side or an angle.
  2. Rerun rectangle / rhombus / kite testsWhat still holds?
  3. Name what brokeThe play’s record.

5Kite and Trapezium

A kite has two pairs of adjacent equal sides. A trapezium (this class’s word) has one pair of parallel sides, as taught. Each name is a test, not a flying-toy photo.

A toy kite shape that fails adjacent-equals is not this kite.

Figure. A kite has two pairs of adjacent equal sides: here the upper pair and the lower pair are each matched, and the pairs differ. A trapezium has exactly one pair of parallel sides — the two horizontal bases on the right. The non-horizontal legs are not parallel.

How it works

  1. For a kite, check adjacent pairsAB=AD and CB=CD, or the taught pairing.
  2. For a trapezium, check exactly one parallel pair as taughtThe parallel test.
  3. Keep the names on the testsNot the photo.

6A definition is a test you can run

Quadrilateral is a test: four sides, closed. If you cannot count four closing sides, you have a broken path, not a quad.

A triangle with an extra tick is not four sides.

Figure. A definition is a test you can run, not a tidy picture. The left rhombus has four equal sides and still fails the right-angle test, so it is not a square. The right square passes both tests. Looks-like is not a reason.

How it works

  1. Count sides that closeFour.
  2. Then run a finer name if askedRectangle, kite…
  3. Start from four sidesThe definition.

7Name the given before the unknown

The given are the marks (ticks, arcs, parallel arrows, right-boxes). The unknown is the name or a missing angle. Read the marks before you say square.

Granting four 90° when only one box is drawn is a silent given.

Figure. Name the given before the unknown. Here ∠A = 60°, ∠B = 120°, ∠C = 60° are given. The unknown is ∠D. Opposite angles of this parallelogram are equal, and the four must sum to 360°, so D is 120° — but the figure leaves D as ?

How it works

  1. Copy the marksThe given.
  2. Name the questionType, or an angle.
  3. Use only those marksGiven first.

8One worked case is enough at this class

One named quad is enough. A page of the same rectangle clone does not add a new 360° rule.

Ten twins of 90-90-90-90 are still one idea.

Figure. One worked case is enough at this class: the same parallelogram with every angle filled. 60 + 120 + 60 + 120 = 360. A second fancy case would not change the test.

How it works

  1. Classify or compute one quadThe case.
  2. A second only if the name changesA check.
  3. StopThis class.
Interior angles of a quadrilateral add to
  1. 360°
  2. 180°
  3. 90°

Two triangles, or the taught total.

Notes

  • The official chapter title is “Quadrilaterals”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • sum of interior angles of a quadrilateral = 360°

Recap

Hold these pegs from the official chapter “Quadrilaterals”. The wording is ExamMaster’s teaching, not a textbook recap.

Rectangles and Squares
A rectangle has four right angles; a square is a rectangle with four equal sides.
Angles in a Quadrilateral
The four interior angles of any simple quadrilateral add to 360°.
Quadrilaterals with Equal Sidelengths
A rhombus has four equal sides. A square is a rhombus with right angles. Equal sidelengths are the rhombus-test; 90° is extra for the square.
Playing with Quadrilaterals
Playing here means a property you can change and re-test: move a vertex, ask which name still holds.
Kite and Trapezium
A kite has two pairs of adjacent equal sides.
A definition is a test you can run
Quadrilateral is a test: four sides, closed.

Practise Quadrilaterals

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