Introduction to Euclid's Geometry — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Introduction to Euclid's Geometry (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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If points A, B, and C are collinear with B between A and C, and AB = 5 cm and BC = 3 cm, find AC.
Answer
Step 1: Since B lies between A and C, we can apply Euclid's axiom that the whole equals the sum of its parts. Step 2: AC = AB + BC (from Euclid's reasoning). Step 3: AC = 5 + 3 = 8 cm. Answer: AC = 8 …
Construct an equilateral triangle on a line segment AB = 6 cm using Euclid's postulates. Which postulates are used?
Answer
Step 1: Draw circle with center A and radius AB = 6 cm (Postulate 3). Step 2: Draw circle with center B and radius BA = 6 cm (Postulate 3). Step 3: Mark intersection point C. Step 4: Draw AC and BC (P…
Two lines l and m intersect at points P and Q. Prove this is impossible using Euclid's axioms.
Answer
Step 1: Assume lines l and m intersect at two distinct points P and Q. Step 2: This means two lines pass through points P and Q. Step 3: But Axiom 5.1 states that only one unique line passes through t…
If AC = BD in the figure where points are arranged as A-C-D-B on a line, prove that AB = CD.
Answer
Step 1: Given AC = BD and points are collinear as A-C-D-B. Step 2: From the arrangement: AB = AC + CD and BD = CD + DB where DB = 0 (since D and B are same relative position). Step 3: Actually, AB = A…
When do you use Euclid's 5th Postulate? Solve: Two lines make angles 70° and 80° with a transversal on the same side. Will they meet?
Answer
Use Euclid's 5th Postulate when checking if two lines will intersect based on angles with a transversal. Step 1: Sum of interior angles on same side = 70° + 80° = 150°. Step 2: Compare with 180°: 150°…
Apply Euclid's Axiom 2: If AB = 7 cm and CD = 7 cm, and we add EF = 3 cm to both, find the new equal lengths.
Answer
Step 1: Given AB = 7 cm and CD = 7 cm, so AB = CD. Step 2: Apply Axiom 2: 'If equals are added to equals, the wholes are equal'. Step 3: AB + EF = 7 + 3 = 10 cm. Step 4: CD + EF = 7 + 3 = 10 cm. Step …
Find the midpoint of line segment AB = 12 cm and prove it's unique using Euclid's principles.
Answer
Step 1: Let C be the midpoint, so AC = CB. Step 2: Since A-C-B are collinear: AB = AC + CB = AC + AC = 2AC. Step 3: Therefore AC = AB/2 = 12/2 = 6 cm. Step 4: To prove uniqueness: Assume another point…
Using Euclid's Postulate 3, draw circles with centers A and B (AB = 8 cm) both having radius 5 cm. Do they intersect? Why?
Answer
Step 1: Apply Postulate 3 to draw circle with center A, radius 5 cm. Step 2: Apply Postulate 3 to draw circle with center B, radius 5 cm. Step 3: Distance between centers = AB = 8 cm. Step 4: Sum of r…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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