Post-assesment | CBSE | G9 | C.5 Euclid's Geometry

A point has _______ dimension.

• One

• Two

• Three

• Zero

The shape of the base of a Pyramid is:

• Triangle

• Square

• Rectangle

• Any polygon

Which of these statements do not satisfy Euclid’s axiom?

• Things which are equal to the same thing are equal to one another

• If equals are added to equals, the wholes are equal.

• If equals are subtracted from equals, the remainders are equal.

• The whole is lesser than the part.

Euclid’s fifth postulate is

• The whole is greater than the part

• All right angles are equal to one another

• If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles

• A circle may be described with any centre and any radius

The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:

• 7

• 8

• 9

• 11

What are the five postulates of Euclid’s Geometry?

If a point C lies between two points A and B such that AC = BC, then prove that AC =1/2 AB. Explain by drawing the figure.

Answer explanation

Given, AC = BC

Now, add AC on both sides.

L.H.S + AC = R.H.S + AC

AC + AC = BC + AC

2AC = BC + AC

Since, we know,

BC +AC = AB (as it coincides with line segment AB, from figure)

∴ 2 AC = AB (If equals are added to equals, the wholes are equal.)

⇒ AC = 1/2 AB.

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Answer explanation

Yes, Euclid’s fifth postulate does imply the existence of the parallel lines. If the sum of the interior angles is equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.

So,

∠1+∠2=180°

Or ∠3+∠4=180°

Look at the figure below. Show that length AH > sum of lengths of AB + BC + CD.

If A, B and C are three points on a line, and B lies between A and C then prove that AB + BC = AC.