In triangle 5, if _n o_ is the base, which side is the perpendicular? LESSON TWENTY-SECOND. REVIEW. Name four acute-angled triangles. (DIAGRAM 17.) Why is the triangle 8 acute-angled? What is an acute-angled triangle? Name three obtuse-angled triangles. Why is the triangle 9 an obtuse-angled triangle? What is an obtuse-angled triangle? Name four right-angled triangles. Why is the triangle 6 a right-angled triangle? What is a right-angled triangle? In the triangle 6, which side is the hypothenuse? Why? What is the hypothenuse? What two sides of the triangle 6 may be regarded as the base? If _q r_ be considered the base, what do you call the side _q s_? Read the hypothenuse of each of the triangles 3, 5, 6, and 11. [Illustration: Diagram 18.] LESSON TWENTY-THIRD. TRIANGLES. (_Continued._) ISOSCELES TRIANGLES. 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? EQUILATERAL TRIANGLES. 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_.