Maths Perimeter and Area part 8 (Triangles with Triangles) CBSE Class 7 Mathematics VII

TL;DR

Triangles inside triangles can have equal areas if they are congruent, but two triangles with equal areas may not be congruent.

Transcript

hello friends this video on perimeter and area part 8 is brought to you by example comm no more fear from exam now one more interesting thing is that that even inside triangles we can find more travel so there are smaller tangles inside a bigger triangle that's interesting right so let us have a look at this one so in this diagram what do you see s... Read More

Key Insights

• 🔺 Triangles can have smaller triangles inside them, and the areas of these smaller triangles can be equal.
• 🟰 The congruence of two triangles determines if their areas are equal or not.
• 📔 Congruent triangles overlap completely, covering equal areas.
• 🔺 Having equal areas in triangles does not always mean that the triangles are congruent.
• 🐕‍🦺 The vice-versa is not true: two triangles with equal areas are not necessarily congruent.
• 🟰 Understanding congruence and equal areas in triangles is important for solving geometry problems.
• 🔺 Knowing the criteria for congruence helps determine if triangles inside a bigger triangle have equal areas.

Questions & Answers

Q: How can smaller triangles inside a bigger triangle have equal areas?

Smaller triangles inside a bigger triangle can have equal areas if they are congruent and overlap completely. If the congruence criteria are met, their areas will be the same.

Q: Why is it important to know if two triangles inside a bigger triangle are congruent?

Knowing if two triangles inside a bigger triangle are congruent is important because it determines if their areas are equal. If they are congruent, the area of each smaller triangle will be half the area of the bigger triangle.

Q: Can two triangles with equal areas always be congruent?

No, two triangles with equal areas may or may not be congruent. Even though congruent triangles have equal areas, the vice-versa is not always true. Their congruence depends on whether they can overlap completely or not.

Q: What is the relationship between congruence and equal areas in triangles?

Congruent triangles have equal areas, but two triangles with equal areas may or may not be congruent. Congruence guarantees equal areas, but equal areas do not necessarily imply congruence.

Summary & Key Takeaways

• Triangles can contain smaller triangles inside them, and the areas of these smaller triangles can be equal to each other.

• For two triangles to have equal areas, they must be congruent and overlap completely.

• Two triangles with equal areas are not necessarily congruent.