Kit Library / Mathematics / Geometry
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
Three sides? Two arcs unlock the triangle.
To construct a triangle when all three side lengths are given, use ruler and compass to find the third vertex by intersecting two arcs.
↳ The intersection of two arcs gives the exact location of the third vertex.
📖 Definition
Three non-collinear points make a triangle.
↳ A triangle has six elements: three sides and three angles.
⚙️ Process
Two circles, one perfect triangle.
An equilateral triangle has all sides equal. Use compass to draw two circles of the same radius from each endpoint of the base.
↳ The intersection of two equal-radius circles gives the third vertex of an equilateral triangle.
⭐ Important Fact
Any two sides beat the third.
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
↳ If the sum of two sides is not greater than the third, no triangle can be formed.
⚠️ Common Mistake
2+3=5? No triangle with 6!
↳ Check the triangle inequality before starting any construction.
➗ Formula
Third side: between difference and sum.
If two sides of a triangle are given, the third side must lie between the difference and the sum of the two sides.
↳ The third side is always greater than the difference and less than the sum of the other two.
📖 Definition
Perpendicular from vertex to opposite side.
↳ An altitude is a perpendicular segment from a vertex to the line containing the opposite side.
⚙️ Process
Arc, intersect, draw perpendicular.
↳ The altitude is constructed by finding the perpendicular from the vertex to the opposite side.
⭐ Important Fact
Three altitudes meet at one point.
The three altitudes of a triangle are concurrent; they meet at a single point called the orthocentre.
↳ The point where all altitudes intersect is the orthocentre.
⚖️ Comparison
Equilateral, isosceles, or scalene?
Scalene: all sides different.
↳ Triangles are classified by the number of equal sides.
⚖️ Comparison
Acute, right, or obtuse?
Obtuse: one angle > 90°.
↳ Triangles are classified by their largest angle.
➗ Formula
All angles add to 180°.
↳ The sum of interior angles of any triangle is always 180°.
⚠️ Common Mistake
Two right angles? Impossible!
↳ Due to the angle sum property, only one angle can be ≥ 90°.
✏️ Example
42° + 17° = 59°, so third is 121°.
↳ Use the angle sum property to find a missing angle.
🌍 Real World
Bridges and buildings rely on triangles.
Triangles are used in bridges, roofs, and cranes because they are rigid and cannot be deformed without changing side lengths or breaking joints.
↳ The rigidity of triangles makes them essential in construction.
Learn to construct triangles using ruler and compass, understand the triangle inequality, classify triangles by sides and angles, and explore key properties like the angle sum and altitudes.
Full explanation, worked examples & memory tricks in the app
All 18 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Three points are said to be non-collinear when:
BeginnerAnswers and explanations are in the Veda app.
Q2. In ∆ABC, which side is opposite vertex A?
BeginnerAnswers and explanations are in the Veda app.
Q3. A triangle has how many elements in total?
BeginnerAnswers and explanations are in the Veda app.
Q4. To construct an equilateral triangle of side 5 cm, you draw two circles. What radius should each circle have?
BeginnerAnswers and explanations are in the Veda app.
Q5. An altitude of a triangle is:
BeginnerAnswers and explanations are in the Veda app.
Q6. The three altitudes of a triangle are concurrent. Their point of concurrence is called the:
BeginnerAnswers and explanations are in the Veda app.
Q7. The sum of the three angles of any triangle is always 180°.
BeginnerAnswers and explanations are in the Veda app.
Q8. Which of these sets of sides CANNOT form a triangle?
IntermediateAnswers and explanations are in the Veda app.
Q9. If two sides of a triangle are 6 cm and 8 cm, the third side must lie strictly between:
IntermediateAnswers and explanations are in the Veda app.
Q10. A triangle has angles 42°, 17° and one unknown angle. What is the unknown angle?
IntermediateAnswers and explanations are in the Veda app.
Q11. In a right-angled triangle, the two acute angles are:
IntermediateAnswers and explanations are in the Veda app.
Q12. A triangle has sides 3 cm, 3 cm and 3 cm. Which description applies?
IntermediateAnswers and explanations are in the Veda app.
Q13. Which set of angles CANNOT be the three angles of a triangle?
IntermediateAnswers and explanations are in the Veda app.
Q14. In an obtuse-angled triangle, what must be done before dropping an altitude from the vertex opposite an obtuse angle's adjacent side?
AdvancedAnswers and explanations are in the Veda app.
Q15. A student constructs a triangle with sides 4 cm, 5 cm and 6 cm by drawing a 6 cm circle from A and a 5 cm circle from B on AB = 4 cm. What is wrong?
AdvancedAnswers and explanations are in the Veda app.
Q16. A triangle has one angle of 95°. Which statement must be true?
AdvancedAnswers and explanations are in the Veda app.
Q17. Given the sides of a triangle are 4 cm, 5 cm, and 6 cm, which of the following statements about constructing this triangle is correct?
AdvancedAnswers and explanations are in the Veda app.
Q18. If two sides of a triangle are 6 cm and 8 cm, what is the range of possible lengths for the third side?
AdvancedAnswers and explanations are in the Veda app.
30 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
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True False
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Memory Match
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Flashcard Battle
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Speed Quiz
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Guess Term
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Sequence Builder
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Categorization
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Revision Battle
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Playable 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.