Euclid's Postulates | Introduction to Euclid's Geometry | Assessment | English | Grade 9

Which of the following statement is false?

• A straight line may be drawn from any one point to any other point.

• A terminated line cannot be produced indefinitely.

• A circle can be drawn with any centre and any radius.

• All right angles are equal to one another.

Answer explanation

A terminated line can be produced indefinitely. Hence, option 2 is the correct answer.

Tags

CCSS.4.G.A.1

Euclid used the term 'postulates' for the assumptions that were specific to _______

• Algebra

• Math

• Pythagoras theorem

• Geometry

Answer explanation

Euclid used the term 'postulates' for the assumptions that were specific to geometry.

How many unique lines can pass through two distinct points?

• Infinitely many lines

• one line

• two lines

Answer explanation

We can draw only one unique line passing through two distinct points.

Tags

CCSS.4.G.A.1

Observe the given figure and tell which of the following options is correct?

• ∠ABC = ∠PQR

• △ABC ≅ △PQR

• ∠ABC ≠ ∠PQR

• △ABC ≆ △PQR

Answer explanation

Here, angle of the both the triangle is 90⁰ and as we know fourth postulate of Euclid's is 'All right angles are equal to one another. Hence, ∠ABC = ∠PQR

Tags

CCSS.8.G.A.2

If two circles are equal, then their radii are equal. The above statement is

• Always true

• Sometimes true

• Never true

Answer explanation

This statement is always true. If you superimpose the region bounded by one circle on the other, then they coincide. So, their centres and boundaries coincide. Therefore, their radii will coincide.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 150°, then the two straight lines, if produced indefinitely, meet on the side on which the sum of angles is

• Less than 150⁰

• Greater than 150⁰

• Is equal to 150°

• Greater than 180°

Answer explanation

Since the sum of interior angle made by two lines is 150⁰ , i.e., less than 180⁰, these will meet on the same side in which the sum of angles is equal to 150⁰. This is based on Euclid's 5th postulate. In the figure, we can see that a straight line LM intersects the lines PQ and RS such that ∠1 + ∠2 = 150⁰. On extending the lines PQ and RS in the same side, they intersect at one point.

Tags

CCSS.8.G.A.5