# Triangles Questions

Triangle questions with answers are provided here for students, which they can practice having a good grasp on the concept. Here, we are presenting problems based on triangles and its related formulas, which students can solve easily. These questions are very basic in nature and are based on Class 6, 7 and 8 syllabuses. Also, Grade 9 and Grade 10 have chapter-Triangles, which explains advance concepts. Check Triangles for Class 9 at BYJU’S.

Triangles are one of the basic geometrical shapes, which we can see in day-to-day life. Thus, it is necessary for children to learn about triangles. The questions here are prepared, so that students cannot only score good marks in academic exams but also in the competitive exams like Maths Olympiads, etc.

## Questions on Triangles with Solutions

The questions here are provided based on the fundamentals of triangles, which students can answer easily. Solving these problems will help them to boost their confidence in a particular concept.

**Q.1. What is a triangle?**

Answer: A triangle is a three-sided polygon, having three vertices and three edges. It is formed by joining three non-collinear points in a two-dimensional plane.

**Q.2. How many types of triangles are there? Name them.**

Answer: There are basically six types of triangles based on sides and angles.

Based on sides: Scalene, Isosceles and Equilateral Triangle

Based on Angles: Acute-angled, Obtuse-angles and Right-angled triangles.

**Q.3. Define scalene triangle, isosceles triangle and equilateral triangle.**

Answer: A triangle which has all its sides unequal, is called a scalene triangle.

A triangle which has two of its sides equal and one unequal is called an isosceles triangle.

A triangle which has all its sides equal is known as an equilateral triangle.

**Q.4. Define acute triangle, obtuse triangle and right triangle.**

Answer: A triangle whose all its angles are less than 90 degrees, is called an acute-angled triangle.

A triangle which has one of its angles more than 90 degrees, is called an obtuse-angled triangle.

A triangle which has one of its angles equal to 90 degrees, is called a right-angled triangle.

Also read: Types Of Triangles

**Q.5. What is the angle sum property of a triangle?**

Answer: The angle sum property of a triangle states that the sum of all the angles of a triangle is always equal to 180 degrees.

**Q.6: If a triangle has its sides equal to 5cm, 4cm and 6cm, then find its perimeter.**

Solution: Given, a = 5cm, b = 4cm, and c = 6cm

Perimeter of a triangle = a+b+c = 5+4+6 = 15cm

**Q.7: If the height of a triangle is 7cm and base length is equal to 10 cm, then find its area.**

Solution: Given,

Height = 7cm and Base = 10 cm

Area of triangle = ½ x b x h = ½ x 10 x 7 = 5 x 7 = 35 cm^{2}

**Q.8: If in a right triangle, the base is 4cm and hypotenuse equal to 5cm, then find the length of its perpendicular. Also, find its area.**

Solution: According to Pythagoras theorem, in a right triangle, we know that,

Hypotenuse^{2} = Base^{2} + Perpendicular^{2}

c^{2} = a^{2}+b^{2}

b^{2}=c^{2}-a^{2}

b^{2}=5^{2}-4^{2} = 25-16 = 9

b = √9 = 3

Now, area of the triangle,

A = ½ b x h

Here, perpendicular is the height of the triangle.

Hence,

Area = ½ x 4 x 3 = 2 x 3 = 6cm^{2}

**Q.9: The side length of an equilateral triangle is 12cm. Find its area.**

Solution: Side of equilateral triangle = 12 cm

Area of equilateral triangle = √3/4 a^{2}

A = √3/4 (12)^{2}

A = 62.35

**Q.10: If two angles of a triangle are 45° and 60°, respectively, then find the third angle.**

Solution: Let ∠A = 45°, ∠B = 60° and ∠C = ?

By the angle sum property we know:

∠A + ∠B + ∠C = 180°

∠C = 180 – ∠A – ∠B

∠C = 180 – 45 – 60

∠C = 75°

Therefore, the third angle is 75°.

### Triangle questions for Class 9

1. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that:

(i) ΔABD ≅ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

2. AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

3. Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A. Show that:

(i) ΔAPB ≅ ΔAQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

4. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB. Show that

(i) ΔDAP ≅ ΔEBP

(ii) AD = BE

5. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB, respectively. Show that these altitudes are equal.

Find the solutions for all the above questions here: Important Questions Class 9 Chapter 7 – Triangles.

### Triangles Questions for Class 10

1. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

2. If ΔABC ~ ΔQRP, ar (ΔABC) / ar (ΔPQR) =9/4 , AB = 18 cm and BC = 15 cm, then PR is equal to

(A) 10 cm (B) 12 cm (C) 20/3 cm (D) 8 cm

3. If the areas of two similar triangles are equal, prove that they are congruent.

4. Sides of triangles are given below. Determine which of them are right triangles.

In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

Find the solutions for the above questions here: Important Questions Class 10 Maths Chapter 6 Triangles