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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-22-INT-01
The Intercept Theorem - Assignment
Chapter: Midpoint Theorem
Topic: The Intercept Theorem
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Equal intercepts on one transversal give equal intercepts on:
  • A.no other line
  • B.any other transversal
  • C.only vertical lines
  • D.the same line
2.
The intercept theorem requires the lines to be:
  • A.equal
  • B.parallel
  • C.perpendicular
  • D.curved
3.
The intercept theorem generalises the:
  • A.Pythagoras theorem
  • B.midpoint theorem
  • C.angle-sum property
  • D.area formula
4.
If $AB=BC$ on one transversal, then $PQ$ ___ $QR$ on another.
  • A.$>$
  • B.$<$
  • C.$=$
  • D.$\ne$
5.
The intercept theorem is also called the ___ theorem.
  • A.equal-intercept
  • B.mid-segment
  • C.angle
  • D.area
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
State the intercept theorem.
7.
Three parallel lines cut $AB=BC=2$ cm on one line; the intercepts on another transversal are:
8.
What property must the lines have?
9.
Which theorem does the intercept theorem generalise?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Three parallel lines make intercepts of $3$ cm each on a transversal; on a second transversal one intercept is $4$ cm. Find the others.
11.
Four parallel lines make equal intercepts of $5$ cm on one transversal. How many equal intercepts on another?
12.
Parallel lines cut a transversal in equal parts; what about another transversal?
13.
If $AB=BC=CD$ on one transversal, then on another $PQ=QR=\ ?$
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Three equally spaced parallel lines cut intercepts of $2.5$ cm each on one transversal. On a second transversal the first intercept is $3$ cm. Find the total length intercepted between the outer lines.
15.
State the intercept theorem and explain briefly how it follows from the midpoint theorem.

Answer Key

Section A — Multiple Choice Questions
  1. (B) any other transversal
  2. (B) parallel
  3. (B) midpoint theorem
  4. (C) $=$
  5. (A) equal-intercept
Section B — Short Answer (2 marks)
  1. Equal intercepts on one transversal give equal intercepts on any other transversal.
  2. Equal.
  3. They must be parallel.
  4. The midpoint theorem.
Section C — Short Answer (3 marks)
  1. $4$ cm each.
  2. $3$ equal intercepts.
  3. It is also cut in equal parts.
  4. $RS$ (all equal).
Section D — Long Answer (5 marks)
  1. $6$ cm (two intercepts of $3$ cm).
  2. Equal intercepts on one transversal give equal intercepts on every transversal; it extends the midpoint theorem (the midline case of a triangle).
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