Class 7 Maths · Original EZT practice
A Tale of Three Intersecting Lines (Class 7 Chapter 7): summary and practice
Three lines meeting in pairs make a triangle - the simplest closed shape. Chapter 7 asks when three lengths can form a triangle, how to construct one and how triangles are named. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 7). Older Class 7 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Triangles from three sides: the triangle inequality
Three lengths form a triangle only if the two shorter ones together are longer than the longest. If their sum equals the longest, they lie flat on a line; if less, they cannot meet.
2. Constructing with sides, then with sides and angles
With three sides given, draw the longest as base, then use a compass to mark arcs of the other two lengths from each end; where the arcs meet is the third vertex. With two sides and the angle between them, draw one side, make the angle at one end and mark the second side's length along it.
3. Altitudes
An altitude is the perpendicular from a vertex to the opposite side (or its extension). Every triangle has three altitudes. In an obtuse triangle an altitude can fall outside the triangle.
4. Types of triangles
By sides: equilateral (three equal), isosceles (two equal), scalene (none equal). By angles: acute (all below ninety), right (one ninety), obtuse (one above ninety). The three angles of any triangle add to one hundred eighty degrees.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Show three lengths can form a triangle
Choose the method: Add the two shorter lengths and compare with the longest.
EZT practice question
Can three cm, four cm and five cm make a triangle?
Show the worked solution
- The two shorter lengths are three and four.
- Their sum is seven, which is greater than five.
- The triangle inequality holds.
Answer: Yes - three plus four is seven, which is greater than five.
Check: The two shorter sides together beat the longest side.
Watch for this: Do not compare the longest with just one short side; the test uses the sum of the two shorter ones.
Now try it yourself
Can sides five, seven and eleven form a triangle?
Check your answer
Yes - five plus seven is twelve, greater than eleven.
The sum of the two shorter sides exceeds the longest.
Show three lengths cannot form a triangle
Choose the method: Same test: add the two shorter and compare.
EZT practice question
Can two cm, three cm and six cm make a triangle?
Show the worked solution
- The two shorter lengths are two and three.
- Their sum is five, which is less than six.
- The two short sides cannot reach each other.
Answer: No - two plus three is five, which is less than six.
Check: When the short sum falls below the longest side, no triangle is possible.
Watch for this: Do not say yes because three positive lengths are given; the inequality decides.
Now try it yourself
Can sides four, four and eight form a triangle?
Check your answer
No - four plus four equals eight, so the sides lie flat on a line.
An equal sum makes a flat, degenerate shape, not a triangle.
Plan a three-side construction
Choose the method: Fix the longest side as base, then intersect arcs of the other two lengths.
EZT practice question
Plan the construction of a triangle with sides four, five and six cm.
Show the worked solution
- Draw the longest side, six cm, as the base.
- From one end, mark an arc of four cm; from the other end, an arc of five cm.
- Where the arcs meet is the third vertex; join it to both ends.
Answer: Base six cm, arc of four cm from one end and arc of five cm from the other - the meeting point is the third vertex.
Check: Each arc fixes the distance from one base end, so the crossing point gives both remaining sides.
Watch for this: Do not draw both arcs from the same end; each arc belongs to one end of the base.
Now try it yourself
What is the first step to construct a triangle given two sides and the included angle?
Check your answer
Draw one of the given sides.
A side must be in place before the angle can be made at its end.
Check constructibility before drawing
Choose the method: Run the triangle inequality first; only construct if it holds.
EZT practice question
Is a triangle with sides three, three and seven constructible?
Show the worked solution
- The two shorter sides are three and three.
- Their sum is six, less than seven.
- The arcs would never meet.
Answer: No - three plus three is six, which is less than seven, so the arcs cannot meet.
Check: The inequality failing means the construction is impossible.
Watch for this: Do not start drawing before checking; impossible side sets waste the attempt.
Now try it yourself
Are sides six, eight and ten constructible?
Check your answer
Yes.
Six plus eight is fourteen, greater than ten.
Find the area from base and altitude
Choose the method: Use half of base times altitude.
EZT practice question
Find the area of a triangle with base ten cm and altitude six cm.
Show the worked solution
- Area is half of base times altitude.
- Ten times six is sixty.
- Half of sixty is thirty.
Answer: Thirty square cm - half of ten times six.
Check: Base and altitude are perpendicular, which is what the area formula needs.
Watch for this: Do not forget the half; base times altitude alone gives the rectangle, not the triangle.
Now try it yourself
Base eight cm, altitude five cm - what is the area?
Check your answer
Twenty square cm.
Half of eight times five is twenty.
Count the altitudes of a triangle
Choose the method: Every vertex has one opposite side, so every vertex gives one altitude.
EZT practice question
How many altitudes does a triangle have?
Show the worked solution
- An altitude runs from a vertex perpendicular to the opposite side.
- A triangle has three vertices.
- So there are three altitudes.
Answer: Three - one from each vertex.
Check: Each of the three vertices provides exactly one.
Watch for this: Do not say one; any side can serve as the base with its own altitude.
Now try it yourself
Where can the altitude of an obtuse triangle lie?
Check your answer
Outside the triangle, on the extension of a side.
The perpendicular from a vertex can fall beyond the opposite side when an angle is obtuse.
Find the third angle and name the type
Choose the method: Subtract the known angles from the angle sum, then classify by angles.
EZT practice question
A triangle has angles of fifty and sixty degrees. Find the third angle and the type of triangle.
Show the worked solution
- The three angles add to one hundred eighty.
- Fifty plus sixty is one hundred ten.
- One hundred eighty minus one hundred ten is seventy - all three are below ninety.
Answer: Seventy degrees; all angles are below ninety, so it is an acute triangle.
Check: Fifty plus sixty plus seventy is one hundred eighty.
Watch for this: Do not call it right-angled without a ninety degree angle.
Now try it yourself
A triangle has angles ninety and thirty-five degrees - find the third and the type.
Check your answer
Fifty-five degrees; a right triangle.
The angle sum gives fifty-five, and the ninety degree angle makes it right.
Find the base angles of an isosceles triangle
Choose the method: Subtract the apex angle, then split the rest equally.
EZT practice question
An isosceles triangle has an apex angle of forty degrees. Find the base angles.
Show the worked solution
- The angle sum is one hundred eighty.
- One hundred eighty minus forty is one hundred forty.
- Base angles are equal: one hundred forty divided by two is seventy.
Answer: Seventy degrees each.
Check: Forty plus seventy plus seventy is one hundred eighty.
Watch for this: Do not divide the full angle sum by two; subtract the apex angle first.
Now try it yourself
What is each angle of an equilateral triangle?
Check your answer
Sixty degrees.
All three are equal and they add to one hundred eighty.
Try a mixed set
Choose a method or explanation before opening each answer.
1. When can three lengths form a triangle?
Show answer and reason
When the two shorter lengths add to more than the longest.
That is the triangle inequality.
2. What is an altitude?
Show answer and reason
The perpendicular from a vertex to the opposite side.
Every triangle has three of them.
3. What is the angle sum of a triangle?
Show answer and reason
One hundred eighty degrees.
It holds for every triangle.
4. Name the types of triangles by sides.
Show answer and reason
Equilateral, isosceles and scalene.
They count three, two and zero equal sides.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Which of these can form a triangle: (a) five, six, ten; (b) two, five, eight; (c) seven, seven, seven?
- Plan the construction of a triangle with sides five, six and seven cm.
- A triangle has angles of thirty and one hundred degrees - find the third angle and name the type.
Know the rule but lose track of the steps?
Bring your book edition, your school topic list and a question you attempted. Ask a tutor to explain the choice of method and test it with a different problem. Agree the lesson topics, schedule and fee before starting.
For cost context, see home tuition fees in Delhi NCR. Agree the topics, schedule and fee with your chosen tutor.
Questions about this practice page
- When can three lengths form a triangle?
- When the two shorter lengths add to more than the longest side.
- What is an altitude?
- The perpendicular from a vertex to the opposite side (or its extension).
- What is the angle sum of a triangle?
- One hundred eighty degrees.
- How many altitudes does a triangle have?
- Three - one from each vertex.
- Are these the NCERT exercise questions for A Tale of Three Intersecting Lines?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.