Identify a triangle and name its parts (sides, angles, vertices)
Classify triangles by their sides — Equilateral, Isosceles, and Scalene
Classify triangles by their angles — Acute-angled, Right-angled, and Obtuse-angled
Understand and apply the Angle Sum Property (sum of all angles = 180°)
Find the missing angle of a triangle when two angles are given
Calculate the perimeter of a triangle
Combine both classifications (e.g., right-angled isosceles triangle)
Identify triangles in real-life objects and structures
Introduction — Triangles All Around Us!
Look around you — triangles are everywhere! The traffic "Give Way" sign on Indian roads is a triangle. The roof of a village hut forms a triangle. The tip of ISRO's rocket nose cone is shaped like a triangle. When you cut a slice of pizza or a sandwich diagonally, you get a triangle. Even the beautiful Rangoli patterns during Diwali use many triangles!
A triangle is the simplest polygon — it has only 3 sides, but it is one of the strongest shapes in nature. Engineers use triangles to build bridges, towers (like the Eiffel Tower), and even roof trusses because triangles do not bend or deform easily. In this chapter, we will learn all about the different types of triangles and their special properties.
What is a Triangle?
A triangle is a closed figure (polygon) made up of three straight line segments. The word "triangle" comes from two Latin words: tri (meaning three) and angulus (meaning angle).
Parts of a Triangle
Sides: A triangle has 3 sides. In ∆ABC, the sides are AB, BC, and CA.
Angles: A triangle has 3 angles. In ∆ABC, the angles are ∠A, ∠B, and ∠C.
Vertices: A triangle has 3 vertices (corners). In ∆ABC, the vertices are A, B, and C.
Naming a Triangle: We name a triangle using its three vertices. For example, a triangle with vertices at points P, Q, and R is written as ∆PQR (read as "triangle PQR"). We can also write it as ∆QPR or ∆RPQ — the starting point can be any vertex, but we go in order around the triangle.
Image needed: A clearly labelled triangle ABC showing all parts — three sides (AB, BC, CA) labelled with different colours, three angles (∠A, ∠B, ∠C) marked with arcs, and three vertices (A, B, C) marked with dots. Include labels pointing to each part. Style: Clean geometric diagram, child-friendly colours, clearly labelled Size: 500×400px
Think About It: Can you draw a triangle with only 2 sides? No! A figure with 2 sides cannot be closed. A triangle is the polygon with the fewest number of sides possible. That is why it is called the simplest polygon.
Types of Triangles — By Their Sides
We can classify triangles based on the length of their sides. There are three types:
1. Equilateral Triangle
An equilateral triangle has all three sides equal in length. The word "equilateral" means "equal sides." Since all sides are equal, all three angles are also equal, and each angle measures exactly 60°.
Example: In ∆ABC, if AB = BC = CA = 5 cm, then ∆ABC is an equilateral triangle.
Each angle: ∠A = ∠B = ∠C = 60°
Total: 60° + 60° + 60° = 180° ✓
2. Isosceles Triangle
An isosceles triangle has two sides equal in length. The word "isosceles" comes from Greek: iso (equal) + skelos (leg). The two equal sides are called the legs, and the third side is called the base. The angles opposite to the equal sides are also equal — these are called base angles.
Example: In ∆PQR, if PQ = PR = 7 cm and QR = 4 cm, then ∆PQR is an isosceles triangle.
The angles at Q and R (base angles) are equal: ∠Q = ∠R.
3. Scalene Triangle
A scalene triangle has all three sides of different lengths. Since no sides are equal, no angles are equal either. Each side and each angle has a different measurement.
Example: In ∆XYZ, if XY = 5 cm, YZ = 7 cm, and XZ = 6 cm, then ∆XYZ is a scalene triangle.
All three angles ∠X, ∠Y, ∠Z are different.
Summary Table — Types by Sides
Type
Sides
Angles
Example
Equilateral
All 3 sides equal
All 3 angles equal (each = 60°)
AB = BC = CA = 6 cm
Isosceles
2 sides equal, 1 different
2 angles equal (base angles)
AB = AC = 5 cm, BC = 3 cm
Scalene
All 3 sides different
All 3 angles different
AB = 4 cm, BC = 6 cm, CA = 5 cm
Image needed: Three triangles shown side by side: (1) Equilateral — all sides marked equal with tick marks, all angles shown as 60°; (2) Isosceles — two sides marked equal, base angles marked equal; (3) Scalene — all sides different lengths, all angles different. Each triangle clearly labelled with its type name below. Style: Clean geometric diagrams, colourful (each type in a different colour), child-friendly Size: 800×350px
Types of Triangles — By Their Angles
We can also classify triangles based on the size of their angles. There are three types:
1. Acute-Angled Triangle
An acute-angled triangle (or simply "acute triangle") is a triangle where all three angles are less than 90°. Every angle is "acute" (sharp and small).
Example: In ∆ABC, ∠A = 70°, ∠B = 60°, ∠C = 50°
All angles are less than 90°, so this is an acute-angled triangle.
Check: 70° + 60° + 50° = 180° ✓
2. Right-Angled Triangle
A right-angled triangle (or "right triangle") has one angle exactly equal to 90°. The side opposite to the right angle is called the hypotenuse — it is always the longest side of the triangle. The other two sides are called legs or arms.
Example: In ∆PQR, ∠Q = 90°, ∠P = 40°, ∠R = 50°
One angle is exactly 90°, so this is a right-angled triangle.
The side PR (opposite to the right angle at Q) is the hypotenuse.
Check: 40° + 90° + 50° = 180° ✓
3. Obtuse-Angled Triangle
An obtuse-angled triangle (or "obtuse triangle") has one angle greater than 90° (and less than 180°). The other two angles must be acute (less than 90°). A triangle can have at most one obtuse angle.
Example: In ∆XYZ, ∠X = 120°, ∠Y = 35°, ∠Z = 25°
One angle (120°) is greater than 90°, so this is an obtuse-angled triangle.
Check: 120° + 35° + 25° = 180° ✓
Summary Table — Types by Angles
Type
Angle Condition
Key Feature
Example Angles
Acute-angled
All 3 angles < 90°
All angles are sharp/small
70°, 60°, 50°
Right-angled
One angle = 90°
Has a hypotenuse (longest side)
90°, 45°, 45°
Obtuse-angled
One angle > 90°
One angle is wide/blunt
110°, 40°, 30°
Image needed: Three triangles shown side by side: (1) Acute-angled — all angles clearly less than 90°, angle values labelled; (2) Right-angled — one 90° angle marked with a small square, hypotenuse labelled; (3) Obtuse-angled — one angle clearly greater than 90°, labelled. Each type named below its diagram. Style: Clean geometric diagrams, different colours for each type, angle arcs shown clearly Size: 800×350px
Think About It: Can a triangle have two right angles? Let's check: 90° + 90° = 180°. That means the third angle would be 0°, which is impossible! So a triangle can have at most one right angle. Similarly, it can have at most one obtuse angle. But it can have three acute angles!
Angle Sum Property of a Triangle
One of the most important properties of a triangle is:
Angle Sum Property
The sum of all three angles of any triangle is always 180°.
This is true for ALL triangles — equilateral, isosceles, scalene, acute, right, or obtuse.
If the three angles are ∠A, ∠B, and ∠C, then: ∠A + ∠B + ∠C = 180°
Proof by Paper Tearing (Activity)
You can prove this property yourself! Here's how:
Draw any triangle on a piece of paper and cut it out.
Label the three angles as 1, 2, and 3.
Tear off the three corners (angles).
Place all three torn angles together with their vertices at the same point.
You will see they form a straight line (180°)!
Image needed: Step-by-step visual showing the angle sum property proof: (1) A triangle with angles labelled 1, 2, 3 in different colours; (2) The three corners torn off; (3) The three torn angles placed together forming a straight line (180°). Show dotted straight line beneath the arranged angles. Style: Step-by-step illustration, colourful torn paper pieces, clearly labelled angles Size: 750×350px
Example 2: In ∆PQR, ∠P = 90° and ∠Q = 38°. Find ∠R.
∠R = 180° − (90° + 38°)
∠R = 180° − 128° ∠R = 52°
(This is a right-angled triangle since ∠P = 90°)
Example 3: In ∆DEF, ∠D = 45° and ∠E = 45°. Find ∠F.
∠F = 180° − (45° + 45°)
∠F = 180° − 90° ∠F = 90°
(This is both a right-angled AND isosceles triangle!)
Example 4: In ∆LMN, ∠L = 110° and ∠M = 30°. Find ∠N.
∠N = 180° − (110° + 30°)
∠N = 180° − 140° ∠N = 40°
(This is an obtuse-angled triangle since ∠L > 90°)
Example 5: In an isosceles triangle ∆ABC, AB = AC and ∠A = 40°. Find ∠B and ∠C.
Since AB = AC, the base angles are equal: ∠B = ∠C.
∠A + ∠B + ∠C = 180°
40° + ∠B + ∠B = 180° (since ∠B = ∠C)
40° + 2∠B = 180°
2∠B = 180° − 40° = 140° ∠B = ∠C = 70°
Example 6: One angle of a triangle is twice the second angle and three times the third angle. Find all three angles.
Let the third angle = x
Then the first angle = 3x, and the second angle = 3x ÷ 2 = 1.5x
Wait — let's try differently. Let the smallest angle = x.
First angle = 3x, Second angle = (3x)/2... This gets tricky. Let's use the given relationship directly:
Let the second angle = a. Then first angle = 2a. Also first angle = 3 × (third angle), so third angle = 2a/3.
Sum: 2a + a + 2a/3 = 180°
(6a + 3a + 2a)/3 = 180°
11a/3 = 180°
11a = 540°
a = 540°/11 ≈ 49.09°...
Hmm, let's pick cleaner numbers. Let the angles be in ratio 2:3:4. Better Example 6: The angles of a triangle are in the ratio 2:3:4. Find all three angles.
Let the angles be 2x, 3x, and 4x.
2x + 3x + 4x = 180°
9x = 180°
x = 20°
The angles are: 2×20° = 40°, 3×20° = 60°, 4×20° = 80°
Check: 40° + 60° + 80° = 180° ✓
Perimeter of a Triangle
The perimeter of a triangle is the total length of its boundary — the distance you would walk if you went all the way around the triangle. It is calculated by adding the lengths of all three sides.
Perimeter Formula
Perimeter = Side 1 + Side 2 + Side 3
If the sides are a, b, and c: P = a + b + c
For an equilateral triangle (all sides = a): P = 3 × a
For an isosceles triangle (two equal sides = a, base = b): P = 2a + b
Example 1: Find the perimeter of a triangle with sides 7 cm, 9 cm, and 5 cm.
P = 7 + 9 + 5 = 21 cm
Example 2: An equilateral triangle has a side of 12 cm. Find its perimeter.
P = 3 × 12 = 36 cm
Example 3: An isosceles triangle has equal sides of 8 cm each and a base of 6 cm. Find its perimeter.
P = 8 + 8 + 6 = 2(8) + 6 = 22 cm
Example 4: The perimeter of a triangle is 45 cm. Two sides measure 15 cm and 18 cm. Find the third side.
Third side = Perimeter − (Side 1 + Side 2)
Third side = 45 − (15 + 18) = 45 − 33 = 12 cm
Example 5: Meena wants to put a ribbon border around a triangular card. The card has sides 20 cm, 15 cm, and 18 cm. How much ribbon does she need?
Ribbon needed = Perimeter = 20 + 15 + 18 = 53 cm
Example 6: An equilateral triangular park has a perimeter of 84 metres. Find the length of each side.
Side = Perimeter ÷ 3 = 84 ÷ 3 = 28 metres
Combined Classification — Sides + Angles
A triangle can be classified by both its sides and its angles at the same time. This gives us several possible combinations:
Type (by sides + angles)
Sides
Angles
Example
Acute-angled Equilateral
All sides equal
All angles = 60° (all acute)
60°, 60°, 60°
Acute-angled Isosceles
Two sides equal
All angles < 90°
70°, 70°, 40°
Acute-angled Scalene
All sides different
All angles < 90°
65°, 55°, 60°
Right-angled Isosceles
Two sides equal (the legs)
One angle = 90°, others = 45° each
90°, 45°, 45°
Right-angled Scalene
All sides different
One angle = 90°
90°, 30°, 60°
Obtuse-angled Isosceles
Two sides equal
One angle > 90°
120°, 30°, 30°
Obtuse-angled Scalene
All sides different
One angle > 90°
100°, 50°, 30°
Image needed: A chart or grid showing the 7 combined types of triangles. Each triangle drawn with its type labelled below (e.g., "Right-angled Isosceles", "Obtuse-angled Scalene"). Arranged in a neat grid format — 3 columns (Equilateral, Isosceles, Scalene) × 3 rows (Acute, Right, Obtuse), with the impossible ones (Right equilateral, Obtuse equilateral) marked with X. Style: Clean classification chart, colourful triangles, educational layout Size: 800×500px
Think About It: Can we have a "right-angled equilateral" triangle? Let's check: if all angles must be 60° in an equilateral triangle, then no angle can be 90°. So NO, a right-angled equilateral triangle is impossible! Similarly, an obtuse-angled equilateral triangle is impossible because all angles must be 60°.
Triangles in Real Life (Indian Context)
Triangles are one of the most useful shapes in everyday life, especially in construction, art, and safety. Here are some real-life examples from India:
Where You See It
Type of Triangle
Why It's Used
Traffic "Give Way" sign
Equilateral (inverted)
Easy to spot from a distance
Roof of a village hut
Isosceles
Rainwater slides off both sides equally
ISRO rocket nose cone
Isosceles (tall, narrow)
Reduces air resistance during launch
Electric pylons / Transmission towers
Many scalene triangles
Triangles make the structure rigid
Rangoli patterns (Diwali)
Equilateral triangles
Create beautiful symmetric designs
Temple Gopuram (tower)
Isosceles (tall)
Draws the eye upward, looks grand
Bicycle frame
Scalene / Isosceles
Makes the frame strong and lightweight
Pizza slice or samosa
Roughly isosceles
Easy to hold, natural shape when cut
Hanger (clothes hanger)
Isosceles
Distributes weight of clothes evenly
Musical instrument: Tanpura base
Triangular cross-section
Acoustic resonance
Fun Fact: The Iron Triangle at Qutub Minar in Delhi refers to the famous iron pillar that has not rusted for over 1600 years! While the pillar itself is cylindrical, the engineering principles used in ancient Indian architecture relied heavily on triangular supports and bracing.
Key Words
Term
Meaning
Triangle
A closed figure with 3 sides, 3 angles, and 3 vertices
Vertex (Vertices)
The corner point(s) where two sides of a triangle meet
Equilateral
A triangle with all 3 sides equal (and all angles = 60°)
Isosceles
A triangle with 2 sides equal (and 2 base angles equal)
Scalene
A triangle with all 3 sides of different lengths
Acute angle
An angle less than 90°
Right angle
An angle exactly equal to 90°
Obtuse angle
An angle greater than 90° but less than 180°
Hypotenuse
The longest side of a right-angled triangle (opposite the 90° angle)
Base angles
The two equal angles in an isosceles triangle
Angle Sum Property
The sum of all 3 angles of a triangle = 180°
Perimeter
The total distance around a triangle (sum of all 3 sides)
By angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°).
The sum of all angles in ANY triangle = 180° (Angle Sum Property).
To find a missing angle: Missing angle = 180° − (sum of other two angles).
In an equilateral triangle, each angle = 60°.
In an isosceles triangle, the base angles are equal.
A triangle can have at most one right angle or at most one obtuse angle.
The hypotenuse is the longest side of a right-angled triangle.
Perimeter = a + b + c (sum of all three sides).
Triangles are the strongest shape in construction — they do not deform.
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. How many sides does a triangle have?
A triangle has 3 sides, 3 angles and 3 vertices.
2. A triangle with all three sides equal is called:
Equilateral = all sides (and all angles) equal.
3. The three angles of any triangle add up to:
Angle sum property: the angles of a triangle always total 180°.
4. A triangle with exactly two equal sides is:
Isosceles = two equal sides.
5. Each angle of an equilateral triangle is how many degrees?
180 ÷ 3 = 60° for each angle.
6. Two angles of a triangle are 60° and 50°. What is the third angle?
180 − (60 + 50) = 180 − 110 = 70°.
7. A triangle with all sides of different lengths is called a ______ triangle.
Scalene = all three sides different.
8. A right-angled triangle has one angle of how many degrees?
A right-angled triangle has one 90° angle.
Practice Questions
A. Fill in the Blanks:
1. A triangle has sides, angles, and vertices.
2. A triangle with all three sides equal is called a(n) triangle.
3. The sum of all angles of a triangle is always .
4. A triangle with one angle equal to 90° is called a triangle.
5. In an equilateral triangle, each angle measures .
6. The longest side of a right-angled triangle is called the .
7. A triangle with all sides of different lengths is called a triangle.
8. In an isosceles triangle, the two equal angles are called angles.
B. Classify the following triangles by their sides:
1. Sides: 5 cm, 5 cm, 5 cm →
2. Sides: 7 cm, 7 cm, 4 cm →
3. Sides: 3 cm, 4 cm, 5 cm →
4. Sides: 10 cm, 6 cm, 10 cm →
5. Sides: 8 cm, 11 cm, 6 cm →
C. Classify the following triangles by their angles:
1. Angles: 60°, 70°, 50° →
2. Angles: 90°, 45°, 45° →
3. Angles: 120°, 35°, 25° →
4. Angles: 80°, 40°, 60° →
5. Angles: 90°, 30°, 60° →
6. Angles: 100°, 50°, 30° →
D. Find the missing angle:
1. In ∆ABC, ∠A = 55° and ∠B = 65°. Find ∠C =
2. In ∆PQR, ∠P = 90° and ∠Q = 42°. Find ∠R =
3. In ∆DEF, ∠D = 38° and ∠F = 72°. Find ∠E =
4. In ∆XYZ, ∠X = 110° and ∠Y = 35°. Find ∠Z =
5. In ∆LMN, ∠L = 60° and ∠M = 60°. Find ∠N =
6. In ∆GHI, ∠G = 25° and ∠I = 90°. Find ∠H =
E. Find the perimeter:
1. A triangle with sides 9 cm, 12 cm, and 7 cm. P =
2. An equilateral triangle with side 15 cm. P =
3. An isosceles triangle with equal sides of 11 cm and base of 8 cm. P =
4. A triangle with sides 6.5 cm, 8.5 cm, and 10 cm. P =
5. The perimeter of a triangle is 36 cm. Two sides are 13 cm and 11 cm. Find the third side =
F. True or False:
1. A triangle can have two right angles.
2. An equilateral triangle is always an acute-angled triangle.
3. A scalene triangle can be right-angled.
4. The hypotenuse is the shortest side of a right-angled triangle.
5. An isosceles triangle has all three angles equal.
6. The sum of any two angles of a triangle is always less than 180°.
7. A triangle can have two obtuse angles.
8. Every equilateral triangle is also an isosceles triangle.
G. Choose the correct answer (MCQ):
1. In a right-angled triangle, the sum of the other two angles is:
a) 180°b) 90°c) 120°d) 60°
2. How many obtuse angles can a triangle have?
a) 0b) 1c) 2d) 3
3. Each angle of an equilateral triangle measures:
a) 90°b) 45°c) 60°d) 120°
4. A triangle with sides 3 cm, 4 cm, and 3 cm is:
a) Equilateralb) Scalenec) Isoscelesd) Right-angled
5. If two angles of a triangle are 75° and 45°, the third angle is:
a) 50°b) 60°c) 70°d) 80°
H. Word Problems:
1. Arjun wants to fence a triangular garden with sides 12 m, 15 m, and 9 m. How much fencing wire does he need?
2. A traffic sign is in the shape of an equilateral triangle. If each side is 45 cm, what is the total length of the border of the sign?
3. In a triangular park, one angle is 90° and another is 50°. What is the third angle? What type of triangle is the park?
4. Priya drew an isosceles triangle where the unequal angle is 80°. Find the two equal base angles.
5. The angles of a triangle are in the ratio 1:2:3. Find all three angles. What type of triangle is it?
6. Dhruv measured a triangular plot of land. Two sides are 25 m and 30 m. If the perimeter is 80 m, what is the length of the third side?
7. Can a triangle be formed with angles 80°, 60°, and 50°? Give a reason.
Activity — Triangle Scavenger Hunt!
Go around your home, school, or neighbourhood and find at least 6 triangles. For each triangle you spot, write down:
#
Object / Place
Type by Sides
Type by Angles
Approximate Measurements
1
Example: Roof of my house
Isosceles
Acute-angled
Sides: ~3 m, 3 m, 4 m
2
3
4
5
6
Bonus Challenge: Cut out a triangle from paper. Tear off its three corners. Arrange them to verify that they form a straight line (180°). Paste it in your notebook!
Want to review the lesson again?
Mathematics
Triangles — Types and Properties
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Identify and name parts of a triangle (sides, angles, vertices)
Classify triangles by sides: Equilateral, Isosceles, Scalene
Classify triangles by angles: Acute, Right, Obtuse
Apply the Angle Sum Property (∠A + ∠B + ∠C = 180°)
Find missing angles and calculate perimeter
What is a Triangle?
A triangle is a closed figure with 3 sides, 3 angles, and 3 vertices. It is the simplest polygon. We name it using its vertices: ∆ABC. Triangles are the strongest shape in construction — they don't deform easily. You see them in traffic signs, rooftops, ISRO rockets, Rangoli patterns, and bicycle frames.
Example 5 (Ratio): Angles in ratio 2:3:4. Find all angles.
2x + 3x + 4x = 180° → 9x = 180° → x = 20°
Angles: 40°, 60°, 80° ✓
Perimeter of a Triangle
Perimeter = Side 1 + Side 2 + Side 3 (P = a + b + c)
Equilateral: P = 3 × side | Isosceles: P = 2(equal side) + base
Example 1: Sides 7 cm, 9 cm, 5 cm → P = 7 + 9 + 5 = 21 cm Example 2: Equilateral, side 12 cm → P = 3 × 12 = 36 cm Example 3: Isosceles, equal sides 8 cm, base 6 cm → P = 8 + 8 + 6 = 22 cm Example 4: P = 45 cm. Two sides: 15 cm, 18 cm. Third side = 45 − 33 = 12 cm Example 5: Equilateral park, P = 84 m. Each side = 84 ÷ 3 = 28 m
Combined Classification (Sides + Angles)
Type
Sides
Angles
Acute Equilateral
All equal
60°, 60°, 60°
Acute Isosceles
Two equal
70°, 70°, 40°
Acute Scalene
All different
65°, 55°, 60°
Right Isosceles
Two equal (legs)
90°, 45°, 45°
Right Scalene
All different
90°, 30°, 60°
Obtuse Isosceles
Two equal
120°, 30°, 30°
Obtuse Scalene
All different
100°, 50°, 30°
[Image: Combined classification chart — grid showing possible triangle types with diagrams]
Note: Right equilateral and obtuse equilateral triangles are IMPOSSIBLE (all equilateral angles must be 60°).
Triangles in Real Life (India)
Object
Triangle Type
Why?
Traffic "Give Way" sign
Equilateral
Easy to spot
Village hut roof
Isosceles
Rain slides equally
ISRO rocket nose
Isosceles (tall)
Cuts air resistance
Electric pylons
Scalene triangles
Makes structure rigid
Rangoli patterns
Equilateral
Symmetric beauty
Bicycle frame
Scalene/Isosceles
Strong and light
Key Words
Term
Meaning
Equilateral
All 3 sides equal, all angles 60°
Isosceles
2 sides equal, 2 base angles equal
Scalene
All sides and angles different
Hypotenuse
Longest side of right-angled triangle
Angle Sum Property
∠A + ∠B + ∠C = 180°
Perimeter
Sum of all 3 sides
Key Points:
• Triangle: 3 sides, 3 angles, 3 vertices. Simplest polygon.
• By sides: Equilateral (all =), Isosceles (2 =), Scalene (all ≠).
• By angles: Acute (all <90°), Right (one =90°), Obtuse (one >90°).
• Angle Sum: Always 180°. Missing angle = 180° − (other two).
• Max 1 right angle OR max 1 obtuse angle per triangle.
• Perimeter = a + b + c. Equilateral: P = 3a.
• Triangles are strongest shape — used in bridges, towers, roofs.
Practice Questions
A. Fill in the Blanks:
1. A triangle has sides, angles, and vertices.
2. A triangle with all three sides equal is called a(n) triangle.
3. The sum of all angles of a triangle is always .
4. A triangle with one angle = 90° is called a triangle.
5. In an equilateral triangle, each angle = .
6. The longest side of a right triangle is the .
7. A triangle with all sides different is called a triangle.
8. In an isosceles triangle, the two equal angles are called angles.
B. Classify by sides:
1. Sides: 5 cm, 5 cm, 5 cm →
2. Sides: 7 cm, 7 cm, 4 cm →
3. Sides: 3 cm, 4 cm, 5 cm →
4. Sides: 10 cm, 6 cm, 10 cm →
5. Sides: 8 cm, 11 cm, 6 cm →
C. Classify by angles:
1. 60°, 70°, 50° →
2. 90°, 45°, 45° →
3. 120°, 35°, 25° →
4. 80°, 40°, 60° →
5. 90°, 30°, 60° →
6. 100°, 50°, 30° →
D. Find the missing angle:
1. ∠A = 55°, ∠B = 65°. ∠C =
2. ∠P = 90°, ∠Q = 42°. ∠R =
3. ∠D = 38°, ∠F = 72°. ∠E =
4. ∠X = 110°, ∠Y = 35°. ∠Z =
5. ∠L = 60°, ∠M = 60°. ∠N =
6. ∠G = 25°, ∠I = 90°. ∠H =
E. Find the perimeter:
1. Sides: 9 cm, 12 cm, 7 cm. P =
2. Equilateral, side = 15 cm. P =
3. Isosceles, equal sides = 11 cm, base = 8 cm. P =
4. Sides: 6.5 cm, 8.5 cm, 10 cm. P =
5. P = 36 cm. Two sides: 13 cm, 11 cm. Third side =
F. True or False:
1. A triangle can have two right angles.
2. An equilateral triangle is always acute-angled.
3. A scalene triangle can be right-angled.
4. The hypotenuse is the shortest side.
5. An isosceles triangle has all three angles equal.
6. A triangle can have two obtuse angles.
7. Every equilateral triangle is also isosceles.
G. MCQ — Choose the correct answer:
1. In a right triangle, the other two angles add up to:
a) 180°b) 90°c) 120°d) 60°
2. How many obtuse angles can a triangle have?
a) 0b) 1c) 2d) 3
3. Each angle of an equilateral triangle =
a) 90°b) 45°c) 60°d) 120°
4. Triangle with sides 3 cm, 4 cm, 3 cm is:
a) Equilateralb) Scalenec) Isoscelesd) Right
5. Two angles are 75° and 45°. Third angle =
a) 50°b) 60°c) 70°d) 80°
H. Word Problems:
1. Arjun fences a triangular garden (12 m, 15 m, 9 m). How much wire needed?
2. Equilateral traffic sign, side = 45 cm. Find border length.
3. Triangular park: one angle = 90°, another = 50°. Find third angle. What type?
4. Isosceles triangle, unequal angle = 80°. Find the two base angles.
5. Angles in ratio 1:2:3. Find all angles. What type of triangle?
6. Two sides: 25 m, 30 m. Perimeter = 80 m. Third side = ?
7. Can angles 80°, 60°, 50° form a triangle? Why?
Activity — Triangle Scavenger Hunt!
Find 6 triangles around you. Write their type and approximate measurements.
#
Object
Type (Sides)
Type (Angles)
Measurements
1
2
3
4
5
6
Bonus: Cut a triangle, tear off 3 corners, arrange to show they make a straight line (180°). Paste in notebook!
You are viewing the worksheet layout. Click Print to save as PDF or print on A4 paper.