Converse of Pythagoras' Theorem

Q.

If the sides of a triangle are 25 cm, 20 cm and 15 cm, then the triangle is right angled.

1. True

2. False

Q.

In a triangle ABC, if AB=2x-1, $AC=2\sqrt{2x}$ and BC=2x+1. Find the angle $\angle BAC$.

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${45}^{\circ }$

4. ${90}^{\circ }$

Q. Explain Pythagoras theorem.

Q.

In triangle ABC, if $BC=AC$ and $\angle B={40}^{\circ }$. Then $\angle C$ is equal to

___ degrees.

Q. Check whether the triangle with the side lengths 5 cm, 7 cm, and 9 cm is an acute, right, or obtuse triangle.

Q. In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find angle BAC. [3 Marks]

Q. $D$ and $E$ are points on the sides $CA$ and $CB$ respectively of a triangle $ABC$ right angled at $C.$ Prove that $A{E}^2+B{D}^2=A{B}^2+D{E}^2$.

Q. In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find the value of angle BAC.

Q. The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. The greatest angle of this triangle is .

1. ${180}^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$
4. ${100}^{\circ }$

Q. In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then find angle BAC.

Q.

A ladder of length 13 m rests against a wall. If it reaches a height of 12 m from the ground, then the distance of the foot of the ladder from the wall is ___ m.

1. 6

2. 5

3. 4

4. 3

Q. In a triangle ABC, if AB=2x-1, $AC=2\sqrt{2x}$ and BC=2x+1. Find the angle $\angle BAC$.

Q. In $△ABC$, $AB=AC$. Side $BC$ is produced to $D$. Prove that ${AD}^2-{AC}^2=BD\times CD$

Q.

The $\angle B$ in the given triangle is ___ degree.

Q. The area of an equilateral triangle is $49\sqrt{3}c{m}^2$. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown in figure. Find the area of the triangle not included in the circle. [Take $\sqrt{3}=1.73$]

1. $5.67c{m}^2$
2. $6.12c{m}^2$
3. $7.77c{m}^2$
4. $7.98c{m}^2$

Q. In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm, then find the value of angle BAC. $\left[3\text{Marks}\right]$

Q. The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. Find the greatest angle of this triangle.

Q.

The measure of $\angle B$ in the given triangle (in degrees) is

Q. The perpendicular from a on side BC of a $\Delta ABC$ intersects BC at D such that DB = 3 CD. Prove that $2A{B}^2=2A{C}^2+B{C}^2$.

Q.

Rahul walks $ 12 m$ north from his house and turns west to walk $ 35 m$ to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?

Friend’s house Rahul’s house 

Q. The sides of a triangle are 3 cm, 4 cm, and 5 cm in length. Then find the greatest angle of this triangle.

Q.

In a △ABC, if AB=2x - 1, AC=$2\sqrt{2x}$ and BC=2x + 1. Find the ∠BAC.

Q. In the above figure, $O$ is a point in the interior of a triangle $ABC,$ $OD\perp BC,OE\perp AC$ and $OF\perp AB$. Show that:
(i) $O{A}^2+O{B}^2+O{C}^2-O{D}^2-O{E}^2-O{F}^2=A{F}^2+B{D}^2+C{E}^2$
(ii) $A{F}^2+B{D}^2+C{E}^2=A{E}^2+C{D}^2+B{F}^2$

Q. State the following statement is True or False
In a right angle triangle $ABC$ such as $AC=5cm,BC=2cm$ , $\angle B={90}^o$
Then the length of $AB$ after construction is $7$cm

1. True
2. False

Q.

In a triangle ABC, if AB = 2x - 1, $AC=2\sqrt{2x}$ and BC = 2x + 1. Find the angle $\angle BAC$.

1. ${60}^{\circ }$

2. ${45}^{\circ }$

3. ${90}^{\circ }$

4. ${30}^{\circ }$

Q.

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${30}^{\circ }$

4. ${45}^{\circ }$

Q.

In a right-angled triangle, the length of the longest side is 10 cm and of another side is 8 cm. What will be the length of the third side?

1. 7 cm
2. 9 cm
3. 5 cm
4. 6 cm

Q. In a right angle triangle ABC right angled at B, if AB = 4 cm, BC = 3 cm, then AC =

1. 5 cm
2. 10 cm
3. 25 cm

Q. Which of the following could form the sides of a right-angled triangle?

1. 9cm, 40cm, 41cm
2. 7cm, 24cm, 25cm
3. 5cm, 12cm, 13cm
4. 20cm, 21cm, 29cm
5. 11cm, 60cm, 61cm
6. 9cm, 39cm, 40cm
7. 8cm, 15cm, 16cm
8. 7cm, 24cm, 26cm

Q. Find the measure of $\angle B$ in the given triangle (in degrees).