CBSE Class 7 · Mathematics
A Tale of Three Intersecting Lines
Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.
This lesson follows the official chapter “A Tale of Three Intersecting Lines” 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 7
- Easy level
- 8 concepts
1Equilateral Triangles
An equilateral triangle has three equal sides and three equal angles (each 60°). The test is equal sides (or equal angles), not a pretty drawing.
A drawing that looks even can still fail a side-measure.
Figure. An equilateral triangle is the three-side test: AB = BC = CA. The three ticks are the same mark because the three visual side lengths match.
How it works
- Measure or construct three equal sidesThe test.
- The three angles match60° each at this class.
- Call it equilateral only after the testNot from a glance.
3Types of Triangles
Types: by sides — equilateral, isosceles (at least two equal), scalene (all different). By angles — acute, right, obtuse. Name the test you are using.
A right-looking corner without a square-test is a guess.
Figure. Side test: equilateral has three matching sides, isosceles has exactly two, scalene has three different lengths. Names follow the test, not a tidy look.
How it works
- Choose sides-test or angles-testOne family at a time.
- Run it on this triangleThis one.
- Name the typeThe sort.
4A definition is a test you can run
“Triangle” here means three segments that close. The definition-test is: three sides, three angles, closed. A two-segment V is not a triangle.
A name on a worksheet is not the closed shape.
Figure. Isosceles is a test: if CA = CB, the base angles at A and B are equal. Ticks on the equal sides are the given; the matching base-angle names are what those ticks force.
How it works
- Count sides that meet end to endThree.
- See a closed interiorThe test.
- If it is open, it is not a triangle yetClose it.
5Name the given before the unknown
The given may be three side-marks or an angle. The unknown may be the type, or a missing equal side. Name the marks you were given before you claim isosceles.
Assuming all sides equal because the chapter said equilateral first is a silent given.
Figure. Name the given first: side AB, side AC, and the included angle at A. BC is the unknown those three determine. SAS is a test, not a pretty triangle.
How it works
- Copy the given marksTicks, or a right-box.
- Name what is askedType, or a length.
- Use only those marksGiven first.
6One worked case is enough at this class
One classified triangle is enough. A page of twins of the same right-isosceles does not add a new type.
Ten copies of 60-60-60 are still one idea.
Figure. Worked case: equilateral side 4. The altitude to the base is 2√3, because height / side = √3/2. The triangle is drawn equilateral; the numbers sit on the brackets.
How it works
- Classify one triangleThe case.
- A second only if the type changesA check.
- StopThis class.
7A miss: swapping the school name for the picture
A mountain photo is a setting. The triangle is the three sides you marked. Measuring the photo’s “look” and skipping the side-test is the swap-miss.
A peak that looks sharp is not automatically acute until angles are tested.
Figure. The miss is pinning “equilateral” on any tidy triangle. The name is earned only when all three sides match. The left triangle has three different visual lengths; the right one has three ticks.
How it works
- Keep the photo as a storyA hill, a roof.
- Mark three sidesThe maths.
- Run the type-test on the marksDo not swap.
8Check by the opposite action or the opposite test
Check a type-claim by the opposite: if you said equilateral, a single unequal side kills it. If you said right, a non-90° corner kills it.
Repeating “it looks equal” is not the opposite test.
Figure. Opposite test: if all three sides match, all three angles match, and the other way around. One tick family is enough to force the other.
How it works
- State the typeThe claim.
- Try to break it with one measureThe opposite check.
- If it breaks, mend the typeHonest.
An altitude of a triangle is
- A perpendicular from a vertex to the opposite side
- Any median you like
- A parallel to a side
90° to the opposite side (or its extension).
Notes
- The official chapter title is “A Tale of Three Intersecting Lines”. 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.
Recap
Hold these pegs from the official chapter “A Tale of Three Intersecting Lines”. The wording is ExamMaster’s teaching, not a textbook recap.
- Equilateral Triangles
- An equilateral triangle has three equal sides and three equal angles (each 60°).
- Constructions Related to Altitudes of Triangles
- An altitude is a perpendicular from a vertex to the opposite side (or its extension).
- Types of Triangles
- Types: by sides — equilateral, isosceles (at least two equal), scalene (all different).
- A definition is a test you can run
- “Triangle” here means three segments that close.
- Name the given before the unknown
- The given may be three side-marks or an angle.
- One worked case is enough at this class
- One classified triangle is enough. A page of twins of the same right-isosceles does not add a new type.
Practise A Tale of Three Intersecting Lines
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device