Classification of Triangles Based on Angles

Q.

The maximum area of a right-angled triangle with hypotenuse $h$ is

1. $\frac{h^2}{2\sqrt{2}}$

2. $\frac{h^2}{2}$

3. $\frac{h^2}{\sqrt{2}}$

4. $\frac{h^2}{4}$

Q.

The area of the isosceles triangle is$\frac{5\sqrt{11}}{4}c{m}^2$ if the perimeter is $11cm$ and the base is $5cm$. Write True or False and justify your answer.

1. True
2. False

Q. ___ number of triangles can be drawn if all the three angles are known.

Q.

If $\sin \left(A\right)=\frac{3}{5}$, what is $\cos \left(A\right),\tan \left(A\right),cosec\left(A\right),\sec \left(A\right),\cot \left(A\right)$?

Q.

Which is the Longest Side of a Right Triangle?

Q.

In an equilateral triangle $ABC$ , if $AD$ is perpendicular to $BC$ , then

1. 

2. 

3. 

4. 

Q.

$△ABC$ is an isosceles triangle with $AC=BC.$ If $A{B}^2=2A{C}^2$ prove that $△ABC$ is a right triangle.

Q.

Which is the longest side in the triangle $PQR$, right - angled at $P$?

Q.

The angle of elevation of the top of a tower from two points distant $s$ and $t$ from its foot are complementary. Prove that the height of the tower is $\sqrt{st}$.

Q.

Question 112

I have three sides. One of my angle measures ${15}^{\circ }$. Another has a measure of ${60}^{\circ }$. What kind of a polygon am I? If I am a triangle, then what kind of triangle am I?

Q. State whether True/False: A triangle which has all the three angles acute that is, less than 90°, is called an acute angled triangle or acute triangle.

1. True
2. False

Q.

Write all the properties of congruence of triangle with their examples?

Q. The triangle in which any one of the angles is a right angle $\left({90}^{\circ }\right)$ is called a right-angled triangle. State whether the statement is true or false.

1. False
2. True

Q.

Question 135

In each of the given pairs of triangles in given figures, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form.

Q.

The following triplets represent the length of sides of the triangle. Use the Pythagoras theorem to check which triplets would make the right triangle.

Note all measures are in cm:

(a)$15,20,25$

(b)$8,9,10$

(c) $2.5,6.5,6$

(d)$16,12,20$

(e)$17,15,8$

(f)$13,14,8$

(g)$7,24,25$

(h)$8,7,12$

Q. State whether true or false: A triangle which has all the three angles less than 90°, is called an acute-angled triangle or acute triangle.

1. False
2. True

Q. In an obtuse triangle what is the remaining two angles

Q.

In an isosceles triangle, which of the following is not true:

1. Two angles are always acute

2. Two angles are equal

3. Two angles are right angles

4. Two sides are equal

Q. If angles in a triangle are in the ratio 1:2:3, then identify the type of triangle?

1. Isosceles right angled triangle
2. Right angled triangle
3. Acute angled triangle
4. Obtuse angled triangle

Q. Every isosceles triangle is also an equilateral triangle.

1. False
2. True

Q.

The area of a square field is $5184m^2$. Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field, and whose length is twice is breadth.

Q.

Question 52

Fill in the blanks to make the statement true.

The longest side of a right-angled triangle is called its ___

Q.

Construct an isosceles right-angled triangle $\mathrm{ABC}$, where $\mathrm{m}\angle \mathrm{ACB}=90°$ and $\mathrm{AC}=6\mathrm{cm}$.

Q. Construct $\Delta PQR$, given $\overline{PQ}=6.5cm,\overline{PR}=7cm$, and $\overline{QR}=8cm$ [3 MARKS]

Q.

The triangle $\mathrm{ABC}$ formed by $\mathrm{AB}=5\mathrm{cm},\mathrm{BC}=8\mathrm{cm},\mathrm{AC}=4\mathrm{cm}$ is

1. an isosceles triangle only

2. a scalene triangle only

3. an isosceles right triangle

4. scalene as well as a right triangle

Q.

A triangle cannot have more than ------------------ obtuse angles.

1. $0$

2. $1$

3. $2$

4. $3$

Q.

What is the hypotenuse in an isosceles right-angled triangle is equal to?

Q. In a right-angled triangle, one of the angles must be equal to __.

1. 145 degrees
2. 180 degrees
3. 90 degrees
4. 120 degrees

Q.

Construct a right angle triangle in which base is $4.5\mathrm{cm}$ and hypotenuse is $6\mathrm{cm}$. Measure its other side. What type of triangle is this according to the sides ?

Q.

A tower subtends an angle $\alpha$ at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b feet just above A is $\beta$. Then, the height of the tower is

1. $b\tan \left(\alpha \right)cot\left(\beta \right)$

2. $bcot\left(\alpha \right)\tan \left(\beta \right)$

3. $bcot\left(\alpha \right)cot\left(\beta \right)$

4. $b{\tan }^2\left(\alpha \right)cot\left(\beta \right)$