LESSON TWENTY-THIRD.

Of the triangle 1, which two sides are equal to each other?

Then it is called an isosceles triangle.

An isosceles triangle is one that has two equal sides.

Name eight isosceles triangles.

Why is the triangle 2 an isosceles triangle?

What kind of a triangle is it on account of its angles?

Then it is an acute-angled isosceles triangle.

Name four acute-angled isosceles triangles.

What kind of a triangle is Fig. 4 on account of the angle k j l?

What kind on account of its equal sides?

Then it is called an obtuse-angled isosceles triangle.

Name one other obtuse-angled isosceles triangle.

What kind of a triangle is Fig. 6 on account of the angle q p r?

What kind on account of its equal sides?

Then it is called a right-angled isosceles triangle.

Name one other right-angled isosceles triangle.

Why is Fig. 12 a right-angled triangle? Why isosceles?

Which of the isosceles triangles has all its three sides equal to each other?

It is called an equilateral triangle.

“Equi” means “equal.” “Latus” means a “side.”

An equilateral triangle is one that has its three sides equal to each other.

What kind of a triangle is Fig. 7 on account of its three equal sides?

What kind on account of its two equal sides s t, s u, or t s, t u, or u s, u t?

Then must not every equilateral triangle be also isosceles?

What kind of a triangle is Fig. 2 on account of its equal sides d e, d f?

If the side e f is longer than either of the other two sides, is it an equilateral triangle?

Then is every isosceles triangle also equilateral?

Name another isosceles triangle that is not equilateral.

Name one that is equilateral.

In any equilateral triangle the three angles are equal to each other.

On account of its equal angles, it is also called an equiangular triangle.

What is Fig. 8 called on account of its three equal sides? On account of its three equal angles?

Every equilateral triangle is also equiangular.

Every equiangular triangle is also equilateral.

Name a triangle that has no two sides equal to each other.

It is called a scalene triangle.

What kind of a triangle is Fig. 5 on account of its right angle?

What kind on account of its three unequal sides?

Then it is a right-angled scalene triangle.

What name can you give Fig. 11 on account of the angle g e f?

On account of its three unequal sides?

Then what may it be called?

Diagram 19.