Geometry Mathematics 2 Shaalaa.com Model Set 1 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Select the appropriate alternative.
In ∆ABC and ∆PQR, in a one to one correspondence \[\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}\] 

∆PQR ~ ∆ABC 

∆PQR ~ ∆CAB 

∆CBA ~ ∆PQR 

∆BCA ~ ∆PQR

Some question and their alternative answer are given.

In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?

15

13

5 

12

Some question and their alternative answer are given.

In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?

15

13

5 

12

Choose the correct alternative answer for the following question.

1 cm³ 

0.001 cm³ 

0.0001 cm³  

0.000001 cm³

Find the distance between the following pairs of point.

W `((- 7)/2 , 4)`, X (11, 4)

Prove that:

`(sin^2θ)/(cosθ) + cosθ = secθ`

∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.

In the given figure, ∠QPR = 90°, seg PM ⊥ seg QR and Q–M–R, PM = 10, QM = 8, find QR.

The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Prove that:

Sin⁴θ - cos⁴θ = 1 - 2cos²θ

In adjoining figure, PQ ⊥ BC, AD ⊥ BC then find following ratios.

1. `("A"(∆"PQB"))/("A"(∆"PBC"))`
2. `("A"(∆"PBC"))/("A"(∆"ABC"))`
3. `("A"(∆"ABC"))/("A"(∆"ADC"))`
4. `("A"(∆"ADC"))/("A"(∆"PQC"))`

In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ² = 4PM² – 3PR².

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse.

Find the height of an equilateral triangle having side 2a.

In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason. 

In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then

1. What is the length of each tangent segment?
2. What is the measure of ∠MRO?
3. What is the measure of ∠MRN?

In the given figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively. Prove that – (1) seg AP || seg BQ,
(2) ∆APR ~ ∆RQB, and
(3) Find ∠ RQB if ∠ PAR = 35°

In the given figure shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and surface area of the toy from the measures shown in the figure (\[\pi = 3 . 14\])

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 8x − 7, DB = 5x − 3, AE = 4x − 3 and EC = (3x − 1), find the value of x.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)

If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.