Introduction to Triangles

Q.

Classify the following statement as true or false.

An isosceles triangle cannot be an obtuse-angles triangle.

1. True
2. False

Q. The smallest number of sides in a polygon is ______.

1. 2
2. 3
3. 4
4. 5

Q. ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Q. Question 8
Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(A) 3.6 cm
(B) 4.1 cm
(C) 3.8 cm
(D) 3.4 cm

Q.

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Q.

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

1. Right angled triangle

2. Isosceles triangle

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

4. Right angled Isosceles triangle

Q. Question 6
If D is a point on the side BC of a $\Delta ABC$ such that AD bisects $\angle BAC$. Then,
(A) BD = CD
(B) BA > BD
(C) BD > BA
(D) CD > CA

Q. Two poles of height, 20 ft and 30 ft are standing at a distance of 10 ft from each other. Find the distance between the tops of these poles.

1. $10\sqrt{3}ft$
2. $10ft$
3. $5\sqrt{2}ft$
4. $10\sqrt{2}ft$

Q. Identify the triangle as equiangular, acute obtuse or right.
(i)
(ii)
(iii)
(iv)
(v)
(vi)

Q.

If there are exactly two sides equal in a triangle, it is known as

1. Scalene triangle

2. Isosceles triangle

3. Equilateral triangle

4. None of these

Q. Fill in the blanks to make the following statements true:

$iv)$ A triangle cannot have more than right angles.

Q. Which of the following can form a triangle?

1. 65, 105, 10
2. 45, 85, 60
3. 95, 15, 80
4. 60, 105, 12

Q. 131.Prove that the line segment joining the middle points of two sides of a triangle is half of third sides

Q. Arrange the following shapes based on the increasing order of the number of sides that are equal.

1. Equilateral $\Delta le$
2. Scalene $\Delta le$
3. Square
4. Isosceles $\Delta le$

Q. Question 65
Fill in the blanks to make the statements true.
The name of a three-sided regular polygon is ___.

Q.

An obtuse-angled triangle is one in which all the angles are less than 90°

1. True
2. False

Q. In $\Delta ABC$, AB = 5 units and AB = BC. Then which of the following statements are true?

1. $\angle A$ = $\angle C$
2. $\angle B$ = $\angle C$
3. BC = 5 units
4. AC = 5 units

Q.

What are the possible locations of the orthocentre of a triangle?

1. Inside the triangle

2. Outside the triangle

3. On the hypotenuse of the triangle

4. On the rectangular vertex of the triangle

Q.

In an equilateral triangle, the sides are ___

Q.

The number of altitudes that can be drawn in a triangle, is

1. $1$

2. $2$

3. $3$

4. $4$

Q. Burst the angles which can form the triangle

1. $30°,60°,90°$
2. $120°,20°,40°$
3. $90°,30°,80°$
4. $110°,50°,70°$
5. $20°,70°,50°$
6. $80°,40°,60°$
7. $70°,50°,60°$
8. $160°,10°,10°$
9. $110°,120°,50°$

Q.

In a right-angled triangle, one acute angle is double the other, then the hypotenuse is

1. Equal to the smallest side

2. Double the smallest side

3. Triple the smallest side

4. None of these

Q. In the following, state if the statement is true(T) or false(F).
A triangle has three sides.

1. True
2. False

Q. The name "equilateral triangle" is based on the side lengths of the triangle.

1. True
2. False

Q. An/A ___ is a triangle that has (at least) two equal side lengths.

1. vertex angle
2. equilateral triangle
3. isosceles triangle
4. obtuse triangle

Q. Question 8
Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(A) 3.6 cm
(B) 4.1 cm
(C) 3.8 cm
(D) 3.4 cm

Q.

Draw the triangles given below. If a particular triangle is not possible, explain why.

Equilateral Obtuse triangle