Pythagorean Theorem

Q.

A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

Q.

Find the sum of the exterior angles in a pentagon.

Q.

If $△ABC$ is an equilateral triangle such that $AD$ is perpendicular to $BC$, then $A{D}^2=$

1. 

2. 

3. 

4. 

Q.

Dot product of two mutual perpendicular vector is

1. $0$

2. $1$

3. $\infty$

4. None of these.

Q. Triangle ABC is a triangle, right angled at $\angle ABC$. If AB = 12cm ; BC = 16cm, find the length of AC.

1. $20cm$
2. $30cm$
3. $25cm$
4. $18cm$

Q. Triangle ABC is a triangle, right angled at $\angle ABC$. If AB = 9cm ; AC = 41cm, find the length of BC.

1. $40cm$
2. $45cm$
3. $50cm$
4. $35cm$

Q.

If $a,b$ and $c$ are sides of a triangle, then $\frac{{[a+b+c]}^2}{[ab+bc+ca]}$always belongs to

1. $[1,2]$

2. $[2,3]$

3. $[3,4]$

4. $[1,3]$

Q.

The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds for all types of triangles.

1. True

2. False

Q.

5cm, 12cm can be two sides of a right-angled triangle.

1. True

2. False

Q.

Pythagoras' theorem holds good for right-angled triangles. State true or false.

1. False

2. True

Q.

Pythagoras theorem holds good for right angled triangles. (True/False)

1. False

2. True

Q.

The hypotenuse of a right-angled triangle is $4m$. If its other sides are equal, find the length of each side.

Q.

State True or False:
'Things which are equal to the same thing are equal to each other'. This statement is an axiom.

1. False

2. True

Q.

In a triangle, sum of squares of two sides is equal to the square of the third side. State whether the statement is True or False.

1. True
2. False

Q.

The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds for all types of triangles. State true or false.

1. True

2. False

Q. For the given right triangle $ABC$, if $AC=10$ units and $BC=8$ units, then

1. $6$ units
2. $7$ units
3. $8$ units

Q.

In the given $∆ABC$ the length of side $AB$ and $AC$ is same$\left(i.eb=c\right)$ and $60°<A<90°$

1. $b<a<b\sqrt{3}$

2. $c<a<c\sqrt{2}$

3. $b<a<2b$

4. $\frac{c}{3}<a<3c$

Q.

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

Q.

According to Pythagoras property:

If in a right angled triangle, perpendicular, base and hypotaneus are a, b and c respectively, then which of the options is true?

1. a² + b² = c²

2. a² - b² = c²

3. a⁴ + b⁴ = c⁴

4. a³ + b³ = c³

Q.

Pythagoras' theorem holds good for right-angled triangles.

1. True

2. False

Q.

$ABC$ is a triangle right angled at $C$. If $AB=25cm$ and $AC=7cm$, find $BC$.

Q. Pythagoras theorem holds good only for ___ angled triangles.

Q.

How Pythagoras property is used

Q. The triangle $DEF$ is right-angled triangle, right-angled at vertex $E$. The relation among the three sides of triangle $DEF$ is given as -

1. $D{F}^2=D{E}^2+E{F}^2$
2. $E{F}^2=D{E}^2+D{F}^2$
3. $D{E}^2=D{F}^2+E{F}^2$
4. $D{F}^2=D{E}^2-E{F}^2$

Q. An isosceles right-angled triangle whose each equal side measures $17$ cm. The measure of third sides is -
$(\text{Given:}\sqrt{2}=1.414)$

1. $24.038$ cm
2. $24$ cm
3. $24.38$ cm
4. $25$ cm

Q. A tree is broken at a height of 5 𝑚 from the ground and its top touches the ground at distance of 12 𝑚 from the base of the tree. Find the original height of the tree.

Q.

Can a triangle be constructed with sides of given lengths?

$4,5,10$

Q. The longest side of a right triangle is called as the Hypotenuse.

1. True
2. False

Q. A ladder 3.7 m long is placed against a wall in such a way that the foot of the ladder is 1.2 m away from the wall. Find the height of the wall to which the ladder reaches.

Q.

The moment Ted heard the name 'Euclid'; he told that he has seen something like Euclid's axioms. Thanks to his habit of always peeking into the books for higher grades! Ted was able to recollect that Euclid gave some axioms. How many axioms did Euclid give?

1. 2
2. 3
3. 4
4. 5