The Elements of Geometry — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for The Elements of Geometry (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts.
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A line segment AB = 8 cm. If point C is the midpoint of AB, and point D is the midpoint of BC, find the length of AD.
Answer
Step 1: Since C is midpoint of AB, AC = CB = AB/2 = 8/2 = 4 cm. Step 2: Since D is midpoint of BC, BD = CD = BC/2 = 4/2 = 2 cm. Step 3: AD = AC + CD = 4 + 2 = 6 cm. Answer: AD = 6 cm. (Using Euclid's …
Using Euclid's postulates, how many lines can pass through two distinct points A and B?
Answer
Step 1: Apply Euclid's 1st postulate - 'A straight line can be drawn from any point to any point'. Step 2: This means exactly ONE unique line passes through two distinct points. Step 3: If we assume t…
Draw a circle with center O and radius 5 cm. Then draw another circle with center P (where OP = 3 cm) and radius 4 cm. Will these circles intersect?
Answer
Step 1: Circle 1 has center O, radius = 5 cm. Circle 2 has center P, radius = 4 cm, OP = 3 cm. Step 2: For intersection, check if |r₁ - r₂| < OP < r₁ + r₂. Step 3: |5 - 4| = 1, and 5 + 4 = 9. So 1 < 3…
If ∠AOB = 90° and ∠COD = 90°, prove that ∠AOB = ∠COD using Euclid's postulates.
Answer
Step 1: Given ∠AOB = 90° and ∠COD = 90°. Step 2: Apply Euclid's 4th postulate: 'All right angles are equal to one another'. Step 3: Since both ∠AOB and ∠COD are right angles (90°), they must be equal.
In triangle ABC, if AB = 6 cm, BC = 8 cm, and AC = 10 cm, verify if this forms a right triangle and find which angle is 90°.
Answer
Step 1: Check Pythagorean theorem: a² + b² = c² (where c is largest side). Step 2: Here, AC = 10 cm is largest. Check if AB² + BC² = AC². Step 3: 6² + 8² = 36 + 64 = 100, and 10² = 100. Step 4: Since …
If PQ = RS and RS = TU, prove that PQ = TU using Euclid's axioms.
Answer
Step 1: Given PQ = RS and RS = TU. Step 2: Apply Euclid's 1st axiom: 'Things which are equal to the same thing are equal to one another'. Step 3: Since PQ = RS and RS = TU, both PQ and TU are equal to…
Construct an equilateral triangle with side length 4 cm using Euclid's postulates. Explain each step.
Answer
Step 1: Draw line segment AB = 4 cm (any two points). Step 2: Using postulate 3, draw circle with center A and radius 4 cm. Step 3: Draw another circle with center B and radius 4 cm. Step 4: Let circl…
If a line segment PQ can be extended to form line l, and another line m intersects l at point R, how many intersection points can l and m have?
Answer
Step 1: Line segment PQ is extended using postulate 2 to form line l. Step 2: Line m intersects line l at point R. Step 3: Apply the theorem: 'Two distinct lines cannot have more than one point in com…
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