M.M: 38 marks Dated: 01/07/2011
Time: 1 hour
Q 1: Fill in the blanks (1 mark per question x 15 = 15 marks)
- Two distinct ______________ lines cannot be parallel to the same line.
- According to Euclid’s fourth postulate, all _____________ angles are equal to one another.
- A terminated _____________ can be produced indefinitely.
- According to Euclid’s seventh axiom, things which are ____________ of the same things are equal to one another.
- According to Euclid’s fourth axiom, things which ______________ with one another are ___________ to one another.
- According to Euclid’s third axiom, if equals are ______________ from equals, the _______________ are equal.
- ______________ are statements which are proved using definitions, axioms, previously proved statements and deductive reasoning.
- ______________ or ____________ are the assumptions which are obvious universal truths and hence are not proved.
- The terms which are taken as undefined by mathematicians are __________, __________ and ____________.
- Two distinct points in a plane determine a ______________ line.
- Two distinct ______________ in a plane cannot have more than one point in common.
- In _____________ geometry, lines are not straight.
- Euclidean Geometry fails on the _____________ surfaces.
- Euclid used the term _____________ for the assumptions that were specific to geometry.
- _______________ means measuring Earth.
Q 2: Write True or False for the following statements. Also write the correct statements for the false statements. (1 mark per question x 6 = 6 marks)
- Two distinct points always determine a line –
- Every ray has a finite length –
- A segment has one end-point only –
- The ray BC is same as ray CB –
- Only a single line can pass through a given point –
- Two lines are coincident if they have only one point in common –
Q 3: What is Playfair’s axiom? How can it be stated in other form? Make a diagram to explain it. (2 marks)
Q 4: If A, B and C are three points on a line and B lies in between A and C, then prove that AB + BC = AC. (2 marks)
Q 5: Give a definition for each of the following terms. (1 mark each x 6 = 6 marks)
- Parallel lines
- Line segment
- Radius
- Straight line
- Plane surface
- Square
Q 6: In the following figure, if PR= QS, then prove that PQ = RS. (2 marks)
Q 7: Write Euclid fifth postulate and explain it with the help of a diagram. (3 marks)
Q 8: What is Euclid’s fifth axiom? Explain it. (2 marks)
