Statement of Pythagoras' Theorem

Q.

In case of right angle triangle, circumradius is given by?

1. two times the hypotenuse.

2. 3 times the hypotenuse

3. half of the hypotenuse.

4. 4 times the hypotenuse

Q.

In a circle of radius 10 cm, a chord subtends a right-angle at the centre, then the length of the chord is

1. 10

2. 20

3. $10\sqrt{2}$

4. $20\sqrt{2}$

Q. Question 13
In figure, arcs have been drawn with radii, 14 cm each and with centres P, Q and R. Find the area of the shaded region.

Q.

In the given figure, the length of side AB is :

1. $3\sqrt{2}units$

2. $2\sqrt{2}units$

3. $4\sqrt{2}units$

4. $\sqrt{2}units$

Q.

According to __ theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Q.

The diagonal of a rectangular field is 16m longer than the shorter side .the longer side is 14 more than the shorter side then find the length of the side of a field.

Q.

ABC is a triangle, D is the mid-point on side BC.



Given, AB=2 cm, AC=4 cm and BD=3 cm
Find the value of AD.

1. 1 cm

2. 3 cm

3. 4 cm

4. 2 cm

Q.

In a triangle PQR right angled at Q if QS = SR then prove that PR² = 4PS² - PQ²

Q. If the ratio of three sides of a triangle is $\sqrt{3}:\sqrt{4}:\sqrt{5},$ then find whether it is a right angle triangle or not.

Q. Question 11 (v)
State whether the following are true or false. Justify your answer.
(v) sin $\theta$ = $\frac{4}{3}$ for some angle $\theta$.

Q. (1)
In Figure, $AD$ is a median of a triangle $ABC$ and $AM\perp BC.$
Prove that :
$\left(i\right)A{C}^2=A{D}^2+BC\times DM+{\left(\frac{BC}{2}\right)}^2$



(2)
In Figure, $AD$ is a median of a triangle $ABC$ and $AM\perp BC.$
Prove that : $\left(ii\right)A{B}^2=A{D}^2-BC\times DM+{\left(\frac{BC}{2}\right)}^2$
(3)
In Figure, $AD$ is a median of a triangle $ABC$ and $AM\perp BC.$
Prove that : $\left(iii\right)A{C}^2+A{B}^2=2A{D}^2+\frac{1}{2}B{C}^2$

Q. A triangle with integral sides is drawn in a circle of radius 5cm so that all the 3 vertices lie on the circle and 2 of them are endpoints of a diameter. Find the area of the triangle in sq.cm.

1. 24

Q.

In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

Q. In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. Find x + y.

1. 10

Q.

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Which of the following is true?

1. AD² + CD² = BD² + AB²

2. AB² + CD² = BC² + AD²

3. None of these

4. AB.BC = AD.DC

Q. Question 6
Write True or False and justify your answer :

If AOB is a diameter of a circle and C is a point on the circle, then $A{C}^2+B{C}^2=A{B}^2$

Q. In a right triangle ABC, $\angle$ B = ${90}^{\circ }$ and sec A = $\frac{5}{3}$. Find sin A.

1. $\frac{5}{3}$
2. $\frac{5}{4}$
3. $\frac{3}{5}$
4. $\frac{4}{5}$

Q.

What is the length of the third side in the above triangle?

1. $\tan \theta$

2. $\cot \theta$

3. $\sec \theta$

4. $\cos \theta$

Q.

AB is the diameter of the circle with centre O. P is a point on the circle such that $PA=2PB.$ If $AB=d,$ find BP.

1. √2d

2. √5d

3. 2√2d

4. d/√5

Q.

AB is the diameter of the circle with centre O. P is a point on the circle such that $PA=2PB.$ If $AB=d,$ find BP.

1. √2d

2. √5d

3. 2√2d

4. d/√5

Q.

In Pythagoras exercise we have questions which says DB=3CD, or something like that is given to us in the question. And with this we find out the measurements of the sides, how to find those lengths.

Q. In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. Find x + y.

Q. Write any two measures of right triangle and write the reason?

Q.

Which of the following are Pythagorean triplets?

1. 4 cm , 6 cm , 8 cm

2. 2 cm , 17 cm , 9 cm

3. 24 cm , 10 cm , 26 cm

4. 13 cm , 27 cm , 30 cm

Q. Match the following if ABC is a right angled triangle at B and D is the foot of perpendicular from B to AC.

1. $AD\times DC$
2. $A{B}^2+B{C}^2$
3. $B{C}^2-AD\times DC$
4. $\Delta ADB$

Q. Match the images on the left with the corresponding unknown sides.

1. $2\sqrt{pq}$
2. $2p^2{q}^2$
3. $2pq$

Q. Assertion :If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is ${45}^o$. Reason: According to Pythagoras theorem, $h^2=l^2+b^2$, $whereh=hypotenuse,l=lengthandb=base.$

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
2. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
3. Assertion is correct, but Reason is incorrect.
4. Assertion is incorrect, but Reason is correct.

Q. In $△ABC$, if AB = 3cm, BC = 4 cm and AC = 5 cm, then $△ABC$ is right angled at A.

1. True
2. False

Q. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of he ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Q.

If the ratio of three sides of a triangle is $\sqrt{3}:\sqrt{4}:\sqrt{5},$ then it is a right angle triangle.

1. True

2. False