Ізосцелес Triangle Properties

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What is an isosceles triangle?

An isosceles triangle is a triangle that has at least two sides of equal length.

What are the equal sides of an isosceles triangle called?

The equal sides of an isosceles triangle are called the legs.

What is the angle called that is between the two legs of an isosceles triangle?

The angle between the two legs of an isosceles triangle is called the vertex angle.

What is the common property of the base angles in an isosceles triangle?

The base angles in an isosceles triangle are equal.

How can you calculate the perimeter of an isosceles triangle?

To find the perimeter, sum up the lengths of the three sides.

What is the property of the altitude drawn from the vertex to the base in an isosceles triangle?

The altitude from the vertex to the base is also the median and the angle bisector.

What theorem is applicable to the angles of an isosceles triangle?

The Base Angles Theorem states that the base angles of an isosceles triangle are congruent.

How do you find the area of an isosceles triangle?

The area can be calculated using the formula: area = 1/2 * base * height.

Given two equal sides and the base angles of 45 degrees, what type of triangle is it?

It's an isosceles right triangle.

If an isosceles triangle has sides of 5 cm, 5 cm, and 8 cm, how do you know it's isosceles?

It has two sides of equal length, 5 cm each, confirming it as isosceles.

What is the relationship between the legs and the base in an isosceles triangle regarding their lengths?

The legs are equal in length, while the base can be of different length.

What formula can you use if given two equal sides and need to find the third, using the angles?

Use the Law of Cosines to find the third side.

Can an isosceles triangle be equilateral?

Yes, if all three sides are equal, it is an equilateral triangle as well.

How does the sum of internal angles in an isosceles triangle compare to any other triangle?

The sum of the internal angles in an isosceles triangle is always 180 degrees, just like any other triangle.

What happens to the altitude if an isosceles triangle is obtuse?

The altitude can fall outside the triangle when extended.





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1. What is an isosceles triangle?

A triangle that has no sides of equal length.

A triangle with three equal angles.

An isosceles triangle is a triangle that has at least two sides of equal length.

A triangle with all sides of different lengths.

2. What are the equal sides of an isosceles triangle called?

The legs.

The hypotenuse.

The bases.

The angles.

3. What is the angle called that is between the two legs of an isosceles triangle?

The base angle.

The vertex angle.

The right angle.

The supplementary angle.

4. What is the common property of the base angles in an isosceles triangle?

They are equal.

They are unequal.

They are obtuse.

They are complementary.

5. How can you calculate the perimeter of an isosceles triangle?

By subtracting the base from twice the sum of the legs.

Sum up the lengths of the three sides.

By adding the legs and dividing by the base.

By only measuring the base.

6. What is the property of the altitude drawn from the vertex to the base in an isosceles triangle?

It is solely an angle bisector.

It intersects the legs.

It is always external.

The altitude is also the median and the angle bisector.

7. What theorem is applicable to the angles of an isosceles triangle?

The Base Angles Theorem.

The Pythagorean Theorem.

Pascal's Theorem.

The Triangle Sum Theorem.

8. How do you find the area of an isosceles triangle?

By multiplying base by height.

Using the sine rule.

Adding the base to the two legs.

Using the formula: area = 1/2 * base * height.

9. Given two equal sides and the base angles of 45 degrees, what type of triangle is it?

It's an isosceles right triangle.

It's an equilateral triangle.

It's a scalene triangle.

It's an obtuse triangle.

10. If an isosceles triangle has sides of 5 cm, 5 cm, and 8 cm, how do you know it's isosceles?

Because all the angles are 60 degrees.

Because the angles are all different.

It has two sides of equal length, 5 cm each, confirming it as isosceles.

Because the base is half of the equal sides.

11. What is the relationship between the legs and the base in an isosceles triangle regarding their lengths?

The base and legs are of equal length.

The legs are equal in length, while the base can be of different length.

The base is always longer than the legs.

The legs are complementary to the base.

12. What formula can you use if given two equal sides and need to find the third, using the angles?

The Law of Perspective.

The Pythagorean Theorem.

Use the Law of Cosines to find the third side.

The Law of Sines.

13. Can an isosceles triangle be equilateral?

No, they are mutually exclusive.

Yes, if all three sides are equal, it is an equilateral triangle as well.

Only if the angles are right angles.

Only if the base angles are obtuse.

14. How does the sum of internal angles in an isosceles triangle compare to any other triangle?

It is always more than 180 degrees.

The sum of the internal angles is always 180 degrees, just like any other triangle.

It is less than in an obtuse triangle.

It can be any value above 100 degrees.

15. What happens to the altitude if an isosceles triangle is obtuse?

The altitude can fall outside the triangle when extended.

The altitude remains inside the triangle.

It becomes impossible to define an altitude.

The altitude is collinear with the base.