SSC (English Medium) इयत्ता ८ वी - Maharashtra State Board Question Bank Solutions for Mathematics

In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.

In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?

Construct the following quadrilateral of given measures.

In ☐ MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58°, m∠O = 105°, m∠R = 90°.

Construct the following quadrilateral of given measures.

Construct ☐ DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.

Construct the following quadrilateral of given measures.

In ☐ ABCD l(AB) = 6.4 cm, l(BC) = 4.8 cm, m∠A = 70°, m∠B = 50°, m∠C = 140°.

Construct the following quadrilateral of given measures.

Construct ☐ LMNO such that l(LM) = l(LO) = 6 cm, l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.

Show the following numbers on a number line. Draw a separate number line for each example.

(1)`3/2 , 5/2 , -3/2`

(2)`7/5 , (-2)/5 , (-4)/5`

(3) `(-5)/8 , 11/8`

(4)`13/10 , (-17)/10`

Observe the number line and answer the questions.

1. Which number is indicated by point B? 
2. Which point indicates the number `1 3/4`?
3. State whether the statement ‘the point D denotes the number `5/2`’ is true or false. 

Show the following numbers on a number line. Draw a separate number line for the example.

`3/2 , 5/2 , -3/2`

Show the following numbers on a number line. Draw a separate number line for the example.

`7/5 , (-2)/5 , (-4)/5`

Show the following numbers on a number line. Draw a separate number line for the example.

`(-5)/8 , 11/8`

Show the following numbers on a number line. Draw a separate number line for the example.

`13/10 , (-17)/10`

The number `sqrt2` is shown on a number line. Steps are given to show `sqrt3` on the number line using `sqrt2`. Fill in the boxes properly and complete the activity.

Activity :

• The point Q on the number line shows the number ______.
• A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
• Right angled ∆ORQ is obtained by drawing seg OR. 

`l  ("OQ") = sqrt2` ,    `l("QR") = 1`

`therefore` by Pythagoras theorem,

`[l("OR")]^2  = [l("OQ")]^2 + [l("QR")]^2 `

= `square^2`+ `square^2` = `square` + `square`

= `square`

∴ l(OR) = `square`

Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number `sqrt3`.

Show the number √5 on the number line. 

Show the number √7 on the number line.

In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the help of the figure.

Corresponding angles.
(1) ∠p and `square`
(2) ∠q and `square`
(3) ∠r and `square`
(4) ∠ s and `square`
Interior alternate angles.
(5) ∠s and `square`
(6) ∠w and `square`

Observe the angles shown in the figure and write the following pair of angles. 

Interior alternate angles 

Observe the angles shown in the figure and write the following pair of angles. 

 Corresponding angles

Observe the angles shown in the figure and write the following pair of angles. 

Interior angles