Triangles and Its Types

Q.

The vectors $3\hat{i}-2\hat{j}+\hat{k}$, $\hat{i}-3\hat{j}+5\hat{k}$ and $2\hat{i}+\hat{j}-4\hat{k}$ form the sides of a triangle. This triangle is?

1. an equilateral triangle

2. an isosceles triangle

3. a right angled triangle

4. collinear

Q. Please answer this Question for me:-

Find the length of the diagonal of a rectangle whose sides are 16cm and 12cm.

Q.

Let $f:R\to R$ be defined by $f\left(x\right)=\left\{\begin{array}{l}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}\right.$. If f has a local minimum at $x=-1$, then a possible value of $k$ is

1. $1$

2. $0$

3. $-1/2$

4. $-1$

Q.

If $AB=3i+j-k$ and $AC=i-j+3k$. If the point $P$ on the line segment $BC$ is equidistant from $AB$ and $AC$, then $AP$ is?

1. $2i–k$

2. $i–2k$

3. $2i+k$

4. None of these

Q. In ΔPQR, Q is a right angle, the lengths of PQ and PR are 8 cm and 17 cm, respectively. Find the length of QR.

1. 13 cm
2. 14 cm
3. 15 cm
4. 16 cm

Q.

ABC is a triangle right angled at C. If AB = 10 cm and AC = 8 cm, find BC.

1. 18 cm

2. 6 cm

3. 2 cm

4. 8 cm

Q. P and Q are two points on the sides AB and AC respectively of triangle ABC, such that AP=3.5cm , PB =7 cm , AQ= 3cm and QC=6cm. If P =4.5cm, find BC

Q.

In the given figure, if AB = AC and D is the midpoint of BC, then triangle ADB is congruent to triangle ADC by congruency.

1. SAS
2. ASA
3. RHS
4. SSS

Q.

Let $S=$ the set of all triangles, $P=$ the set of all isosceles triangles, $Q=$ the set of all equilateral triangles, $R=$ and the set of all right-angled triangles. What do the sets $P\cap Q$ and $R-P$ represents respectively?

Q.

In the given figure $ABC$ is a right-angled triangle at B. Let $D$ and $E$ be any points on $AB$ and $BC$ respectively. Prove that ${\left(AE\right)}^2+{\left(CD\right)}^2={\left(AC\right)}^2+{\left(DE\right)}^2$

Q.

Classify the following triangles according to measures of angles.

$40°,90°,50°$

Q.

The perimeter of a right angled triangle is 160cm and its sides are in the ratio 8:15:17. Then find its hypotenuse.

Q. If AB = 3.5 cm, BC = 7 cm, and AC = 10 cm. Which criterion can be used to construct ABC?

1. SSS
2. SAS
3. ASA
4. RHS

Q. Find the length of a line segment, say AB, if its perpendicular bisector intersects it at point M, 6 cm from A.
(1 mark)

Q.

What is the measure of each angle in an equilateral triangle?

Q.

Construct an isosceles triangle with equal sides 3.6 cm and
third side 5.5 cm.

Q. What is the length of x in the given figure?

1. 12 cm
2. 22 cm
3. 14 cm
4. 8 cm

Q. In the given isosceles right-angled triangle, find x.

1. 3 cm
2. 6 cm
3. 9 cm
4. 6.5 cm

Q.

A triangle whose two angles measure ${25}^{\circ }$ and ${35}^{\circ }$ is ___ triangle.

1. an acute angled

2. an obtuse angled

3. a right angled

4. an equilateral

Q. Which is the included angle between the sides DE and EF of △DEF?

1. ∠E
2. ∠F
3. None of the above
4. ∠D

Q. $\text{Which of the following is correct about}\text{the}△ABC?$

1. Isosceles
2. Equilateral
3. Acute
4. Scalene

Q. Which of these can be an angle in an equilateral triangle?

1. 30 degrees
2. 90 degrees
3. 60 degrees
4. 120 degrees

Q.

In the given figure, name the following -

1. side opposite to the vertex ‘ P ’ of the $△PQR$
2. angle opposite to the side PR
3. vertex opposite to the side QR

Q.

If the angles of a triangle are 30°, 30° and 120°, then the triangle is ___.

1. an acute angled triangle

2. a right angled triangle

3. an obtuse angled triangle

4. a equilateral triangle

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

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

Q. If exactly two sides of the triangle are equal, then the triangle is ___.

1. scalene
2. isosceles
3. equilateral
4. right-angled

Q.

The side opposite to vertex B in a triangle ABC is ______

1. AB

2. AC

3. AB and BC

4. BC

Q.

Which of the following triangles are isosceles as well as obtuse-angled triangles?

1. Fig 1 and Fig 3 only

2. Fig 1, Fig 2 and Fig 4 only

3. Fig 2 and Fig 3 only

4. Fig 1, Fig 2 and Fig 3 only

Q.

A triangle in which each angle is less than 90 degrees is called ___.

1. a scalene triangle

2. an acute-angled triangle

3. an obtuse-angled triangle

4. a right-angled triangle

Q. It is possible to have a right-angled equilateral triangle.

1. True
2. False