Example 1
A triangle has side lengths 7 cm, 7 cm, and 10 cm. What type of triangle is it based on its sides?
- Observe that two sides are equal to 7 cm.
- A triangle with two equal sides is called isosceles.
Answer: Isosceles
📗 Class 7 maths · session 6 of 12 · 60 minutes · 🎁 free with an account
Triangles and their properties
Welcome to another superhero math mission with Captain Calc. Today we will explore triangles and master all their secret properties together.
🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up3 min
- Warm-up games5 min
- Types of Triangles, Medians, and Altitudes8 min
- Angle Sum Property of a Triangle7 min
- Exterior Angle of a Triangle7 min
- Side Inequality and Pythagoras Theorem7 min
- Angle Detective Mission6 min
- Triangle Builder Challenge5 min
- Pythagoras Rescue Mission6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Classify triangles by sides and angles and identify medians and altitudes.
- Apply the angle sum property of a triangle to find unknown angles.
- Use the exterior angle property to calculate interior and exterior angles.
- Test side length conditions and solve right triangles using Pythagoras theorem.
Before you start
- Understanding basic line segments and angles.
- Basic addition, subtraction, and squaring of numbers.
Have ready
- A notebook and a pencil.
- A ruler for drawing straight line segments.
Class 7 · CBSE, ICSE and state boards
Warm-up · think first
A shape has 3 sides and 3 interior angles. If two angles are 50° and 60°, what is the third angle in degrees?
Show the answer
70. The sum of all three interior angles in any triangle must equal 180°.
Teacher tip: Ask students to recall what happens when you add all three corner angles together.
🎮 Warm-up games · 5 quick games
Play with Captain Calc
Six minutes with Captain Calc. Vote, say why, then show the answer.
- Which set of side lengths does not belong? (3 cm, 4 cm, 5 cm · 5 cm, 12 cm, 13 cm · 6 cm, 8 cm, 10 cm · 2 cm, 3 cm, 6 cm)
Answer: 2 cm, 3 cm, 6 cm does not belong because 2 + 3 is not greater than 6, so these lengths cannot form a triangle. - Would you rather calculate the missing angle of a triangle using the angle sum property (A) or check if three side lengths can form a triangle (B)? (A · B)
Answer: Both choices use quick mental math tricks to test geometric rules! - The measure of an exterior angle of a triangle is equal to the sum of its two interior opposite angles. (Always · Sometimes · Never)
Answer: Always. This is a fundamental property of every triangle. - I am an isosceles triangle. One of my equal angles is 50°. What is the measure of my vertex angle in degrees?
Answer: 80. The equal angles sum to 50° + 50° = 100°. Subtracting from 180° leaves 80°. - Where do you see triangles in real-world structures like bridges or roofs, and why do engineers use them?
Answer: Triangles are used in roof trusses, cranes, and bridges because a triangle is a rigid shape that does not warp easily under pressure.
Part 1 of 4 · learn, see, practise
Types of Triangles, Medians, and Altitudes
Triangles can be classified by side lengths as equilateral, isosceles, or scalene. They are also classified by angles as acute, right, or obtuse.
A median is a line segment connecting a vertex to the midpoint of the opposite side. An altitude is a perpendicular line segment drawn from a vertex to the opposite side.
Example 2
How many medians can be drawn in any single triangle?
- Every triangle has 3 vertices.
- From each vertex, exactly 1 median can be drawn to the opposite side.
Answer: 3
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- Equilateral
- 3
- Median
- Right-angled
- Isosceles
- 90
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Unlocking the rest of this lesson gives you:
- Part 2: Angle Sum Property of a Triangle, with practice at three levels
- Part 3: Exterior Angle of a Triangle, with practice at three levels
- Part 4: Side Inequality and Pythagoras Theorem, with practice at three levels
- Class activity 1: Angle Detective Mission
- Class activity 2: Triangle Builder Challenge
- Class activity 3: Pythagoras Rescue Mission
- A 10-question quiz
- After-class project: Designing a Triangular Superhero Tower
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Triangles and their properties: questions
What is the difference between a median and an altitude of a triangle?
A median connects a vertex to the midpoint of the opposite side, while an altitude is a line drawn from a vertex perpendicular to the opposite side.
Can a triangle have two right angles?
No, because two 90 degree angles add up to 180 degrees, leaving 0 degrees for the third angle.
How do I know which side is the hypotenuse in a right triangle?
The hypotenuse is always the longest side and is directly opposite to the 90 degree right angle.
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