Triangles Class 7 Worksheet — Free PDF Download with Answers

Some chapters need you to hold a pencil. Triangles are one of them. The muscle of geometric intuition grows when a student draws a triangle, labels its vertices and marks the angles with their own hand. No clever app can replicate the feel of a ruler moving across paper or the small satisfaction of marking the right angle with a neat square.

I taught geometry to a Class 7 boy last year who could solve every triangle problem on his school learning app but struggled on the written mock test. His issue was not understanding. It was that on paper he kept forgetting to show the angle sum as $180\degree$ or to mark the sides as equal. Two weeks of worksheet practice fixed him. By the unit test he was writing the cleanest geometry in the class.

Worksheets also teach patience. Triangle questions often need you to combine several rules in sequence — angle sum, exterior angle, isoceles property. Working through such a question on paper, with space to think, develops the kind of structured thinking that exams reward.

Another reason worksheets shine for triangles is the answer key. After a tricky question, a student can immediately confirm the answer and trace back through their working. They learn to check not only the final number but the reasoning at each step.

And there is the rest from screens. Thirty minutes with paper, a pencil and an eraser is a welcome change from the blue light of a tablet.

The full Class 7 triangles chapter is covered across all three boards.

Topics included:

* Types of triangles by sides (scalene, isoceles, equilateral)
* Types of triangles by angles (acute, right, obtuse)
* Angle sum property
* Exterior angle and its property
* Triangle inequality (sum of two sides greater than the third)
* Pythagoras theorem (introductory for right triangles)
* Medians and altitudes (introduction)

Level breakdown:

Total 60 questions, with a complete answer key at the end of the PDF.

Before diving into the worksheet, revise these properties.

* Angle sum property — The three angles of any triangle add up to $180\degree$.
* Exterior angle theorem — An exterior angle of a triangle equals the sum of the two opposite interior angles.
* Triangle inequality — The sum of any two sides of a triangle is greater than the third side.
* Isoceles triangle — Two sides equal, two angles equal (the angles opposite the equal sides).
* Equilateral triangle — All three sides equal, all three angles equal to $60\degree$.
* Right triangle — One angle is $90\degree$. The sum of the other two is $90\degree$.
* Pythagoras theorem — In a right triangle with legs $a, b$ and hypotenuse $c$: $a^2 + b^2 = c^2$.
* Median — A line from a vertex to the midpoint of the opposite side.
* Altitude — A perpendicular from a vertex to the opposite side.

Quick tip: In any isoceles triangle problem, the two base angles are always equal. If you know one of the equal angles and the apex, you can find the other equal angle in one step.

Level 1 — Easy

1. Two angles of a triangle are $50\degree$ and $60\degree$. Find the third angle.
Solution: $180 - 50 - 60 = 70\degree$.

2. Classify a triangle with all sides $7$ cm.
Solution: All sides equal, so equilateral.

3. Can a triangle have angles $90\degree$, $60\degree$, $40\degree$?
Solution: Sum is $190\degree$, which is more than $180\degree$. So no.

Level 2 — Medium

1. The exterior angle of a triangle is $120\degree$. The two opposite interior angles are in the ratio $2 : 3$. Find them.
Solution: Sum is $120\degree$. Let the angles be $2x$ and $3x$. $5x = 120$, so $x = 24$. Angles are $48\degree$ and $72\degree$.

2. Can a triangle have sides $5$ cm, $8$ cm and $15$ cm?
Solution: $5 + 8 = 13 < 15$. Triangle inequality fails. So no.

3. In an isoceles triangle, the apex angle is $40\degree$. Find each base angle.
Solution: Base angles are equal. Sum of all three is $180\degree$. So each base angle is $\dfrac{180 - 40}{2} = 70\degree$.

Level 3 — Hard

1. In a right triangle, the legs are $9$ cm and $12$ cm. Find the hypotenuse.
Solution: $h^2 = 9^2 + 12^2 = 81 + 144 = 225$. So $h = 15$ cm.

2. In triangle $ABC$, $\angle A = 2x$, $\angle B = x + 10$, $\angle C = x - 10$. Find $x$.
Solution: Sum is $180$: $2x + x + 10 + x - 10 = 180$, so $4x = 180$ and $x = 45$.

3. A ladder $13$ m long reaches a window that is $12$ m above the ground. How far is the foot of the ladder from the wall?
Solution: This is a right triangle with hypotenuse $13$ and one leg $12$. Let the other leg be $d$. Then $d^2 = 169 - 144 = 25$, so $d = 5$ m.

1. Print — Use a desk and keep a ruler handy.
2. Warm up — Draw five different triangles (scalene, isoceles, equilateral, right, obtuse) and label the angles.
3. Time yourself — 15 minutes for Level 1, 25 for Level 2, 35 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redraw the figure for every wrong answer and solve again.
6. Try again — Next day, redo wrong questions.

Daily plan: 25 minutes a day for two weeks.

Weekly revision: On Sundays, draw a triangle with three given conditions (like two sides and one angle) and verify the triangle inequality.

1. Forgetting angle sum is 180 — Students sometimes think the sum is $360\degree$ (confusing with quadrilaterals) or skip adding altogether.

2. Wrong exterior angle formula — The exterior angle is the sum of the two opposite interiors, not the sum of all three.

3. Ignoring triangle inequality — Drawing a triangle with impossible side lengths. Always check that the sum of any two sides is greater than the third.

4. Assuming isoceles — Students assume that if two sides look equal in a drawing, they are. Only use the given measurements.

5. Pythagoras errors — Mixing up the hypotenuse and the legs. The hypotenuse is the longest side, opposite the right angle.

6. Unit confusion — Forgetting to write cm or m in the answer. Exam markers deduct half a mark for missing units.

CBSE (NCERT)
Triangle and Its Properties is Chapter 6 of NCERT Class 7. Weightage is around 12 marks. Questions focus on angle sum, exterior angle and properties of isoceles and equilateral triangles.

ICSE (Selina / ML Aggarwal)
ICSE Class 7 covers the same topics plus introductory Pythagoras. Weightage is around 15 marks. Questions demand clear step by step working and reasons.

IB MYP
IB MYP introduces triangles as part of geometry exploration. Students investigate properties through measurement and construction, then generalise. Pythagoras may be introduced through real world applications.

Download the free Class 7 Triangles worksheet:

* Triangles CBSE Worksheet
* Triangles ICSE Worksheet

Online practice:

* Triangles Online — CBSE
* Triangles Online — ICSE

* AI Maths Solver — Get step by step triangle solutions from a photo.
* Spark Coach — AI tutor with hints.
* Class 7 Maths Complete Guide
* All Worksheets Hub
* Class 7 Formulas

Week 1: Properties and classification

* Day 1: Read the chapter and draw each triangle type.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 angle sum and exterior angle questions.
* Day 5: Level 2 isoceles and inequality questions.
* Day 6: Redo wrong answers.
* Day 7: Rest.

Week 2: Advanced and Pythagoras

* Day 8: Level 3 questions 1 to 10.
* Day 9: Pythagoras questions from Level 3.
* Day 10: Redo wrong Level 3 answers.
* Day 11: Construct three triangles using given angles and measure sides.
* Day 12: Mixed quiz.
* Day 13: Mock test (45 minutes).
* Day 14: Review.

* Class 7 Lines and Angles Worksheet
* Class 7 Congruence Worksheet
* Class 7 Symmetry Worksheet
* Class 7 Perimeter and Area Worksheet
* Class 7 Maths Complete Guide