Right Angled Triangle

Q.

In a right triangle ABC, right-angled at B, the longest side is ___?

1. None of these

2. AB

3. AC

4. BC

Q.

What means orthogonal?

Q.

Consider a right triangle ABC, right-angled at B. Then,

1. None of these

2. AB

3. BC

4. AC

Q.

Two lines are perpendicular if they intersect each other at:

1. acute angle

2. right angle

3. obtuse angle

4. none of these

Q.

In an isosceles right triangle ABC, right-angled at B, the longest side is ___?

1. AC

2. AB

3. BC

4. None of these

Q.

$△$ ABC is a right angled triangle, right angled at B and the perpendicular drawn from B to the opposite side bisects it at D. BD = ___ cm, if AD = DC = 5 cm.

Q. How many right angled triangles with co-prime integer sides and base of length 28 cm are there?

Q.

What are $2$ perpendicular lines?

Q.

In ΔPQR, S is any point on the side QR. Show that PQ + QR + RP $>$ 2 PS

Q.

If $JK$ perpendicular $LM$ which statement is true.

1. $JK$ and $LM$ are not in the same plane

2. $JK$ and $LM$ meet at a $90°$ angle

3. .$JK$ and $LM$ meet at a $45°$ angle

4. $JK$ and $LM$ are coplanar and do not intersect

Q. Question 6
S is any point on side QR of a $\Delta PQR$. Show that PQ + QR + RP > 2 PS.

Q. In a right triangle ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. If AC = 2AB, what is the area of $\Delta$ ABD? given, area of $\Delta$ ABC = 5 sq units.

1. 0.5 sq. unit
2. 1 sq. unit
3. 1.25 sq. unit
4. 5 sq. unit

Q. Question 10
Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give the reason for your answer.

Q.

In a right angle triangle $\Delta ABC$, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $\Delta ABD$ and $\Delta BCD$?

1. ${\left(\frac{AD}{BD}\right)}^2$

2. ${\left(\frac{AB}{BC}\right)}^2$

3. ${\left(\frac{AB}{AC}\right)}^2$

4. ${\left(\frac{BD}{DC}\right)}^2$

Q.

In a right triangle $\Delta ABC$ with right angle at B and BD is a perpendicular dropped onto the hypotenuse. If AC = 2AB, what is the area of $\Delta ABD$? (area of $\Delta ABC$ = 5 sq units.)

1. 1 sq. unit

2. 0.5 sq. units

3. 1.25 sq. units

4. 5 sq. units

Q.

In any $\Delta$ABC where $\angle$ B=90${}^{\circ }$, ${\sin }^{2}A$ + ${\cos }^{2}C$ = 1.

1. True

2. False

Q. In a right $\Delta ABC$ with right angle at B, BD is a perpendicular dropped onto the hypotenuse. If AC = 2AB, what is the area of $\Delta ABD$?
Note: Area of $\Delta ABC$ = 5 sq units

Q. In a triangle ABC right angled at B,
$\angle ACB=\theta .$

$\text{If}tan\theta =\frac{5}{12}$,
$\text{then find the value of}\frac{(1+cos\theta )\times (1-sin\theta )}{(1+sin\theta )\times (1-cos\theta )}.$

1. $\frac{100}{9}$
2. $\frac{91}{18}$
3. $\frac{84}{27}$
4. $\frac{12}{5}$

Q.

In $△$ABC, ∠ABC = 90${}^{\circ }$ ∠BAC = 45${}^{\circ }$ ∠ACB = 45${}^{\circ }$. What is this triangle called?

1. Right angled triangle

2. Isosceles triangle

3. 90^o triangle

4. Right angled Isosceles triangle

Q.

Perpendicular lines make right angle, i.e., ${90}^{\circ }$ with each other.

1. True
2. False

Q.

$X$is a point on the side $BC$ of $△ABC$ Use the symbols $>,<\text{or}=$ to make the following statements true:

$AX\underline{}AB+BX$

Q. If triangle ABC is right angled at B and
$sinA=\frac{3}{5}$, then find the value of cos A.

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

Q. In a triangle ABC right angled at B,
$\angle ACB=\theta .$
$\text{If}tan\theta =\frac{3}{4},\text{then find}sin\theta$.

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

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

1. $sin\theta$
2. $cot\theta$
3. $sec\theta$
4. $cos\theta$

Q.

Length of the altitude on the hypotenuse of a right angled triangle with area A $c{m}^2$ and one of the sides equal to b cm, is

1. $\frac{2b}{\sqrt{b^4+4A^2}}$

2. $\frac{2A{b}^2}{\sqrt{b^4+4A^2}}$

3. $\frac{2b^{2}A}{\sqrt{b^4+A^2}}$

4. $\frac{2bA}{\sqrt{b^4+4A^2}}$

Q.

In a right triangle $\Delta ABC$ with right angle at B and BD is a perpendicular dropped onto the hypotenuse. If AC = 2AB, what is the area of $\Delta ABD$? (area of $\Delta ABC$ = 5 sq units.)

1. 0.5 sq. units

2. 1 sq. unit

3. 1.25 sq. units

4. 5 sq. units

Q.

In the given right angle triangle, if $Sin\theta =\frac{3}{5}$, then find the value of $3tan\alpha$.

1. 5

2. 1

3. 4

4. 3

Q. In $\Delta ABC,\angle A={12}^o$ and $\angle C={97}^o$. Arranging the sides (according to lengths) in ascending order, we get:

1. $BC<AB<AC$
2. $AB<AC<BC$
3. $BC<AC<AB$
4. $AB<BC<AC$

Q. What is area of equilateral triangle?

Q.

Two lines are perpendicular if they make an angle of $—$