Which pentagon has one side longer than any one of its other sides? Which has its sides all equal to each other? Are its angles also equal? It is therefore a _regular polygon_, or _regular pentagon_. Name a hexagon that is not regular. Name a regular hexagon. A regular octagon. A regular heptagon. _A polygon is a plane figure bounded by straight lines._ LESSON TWENTIETH. REVIEW. Name all the triangles. (DIAGRAM 16.) Why is Fig. A a triangle? What is a triangle? What other name is sometimes given to triangles? Name all the quadrilaterals. Why is Fig. B a quadrilateral? What is a quadrilateral, or quadrangle? Name all the pentagons, hexagons, heptagons, octagons, and nonagons. Why is C a pentagon? What is a pentagon? A hexagon? A heptagon? &c. How many polygons in the diagram? What is a polygon? If each side of Fig. B is one inch, how many inches are there in its perimeter? When is a polygon regular? Name all the regular polygons in diagram 16. Name all the irregular polygons. [Illustration: Diagram 17.] LESSON TWENTY-FIRST. TRIANGLES. ACUTE-ANGLED TRIANGLES. In the triangle 1, what kind of an angle is _b a c_? _a c b_? _c b a_? (DIAGRAM 17.) Then it is called an _acute-angled triangle_. _An acute-angled triangle is one whose angles are all acute._ Read three other acute-angled triangles. OBTUSE-ANGLED TRIANGLES. In the triangle 4, what kind of an angle is _l k m_? Then it is called an _obtuse-angled triangle_. _An obtuse-angled triangle is one that has one obtuse angle._ Name two others. RIGHT-ANGLED TRIANGLES. In the triangle 3, what kind of an angle is _g i j_? Then it is called a _right-angled triangle_. _A right-angled triangle is one that has one right angle._ Name three other right-angled triangles. Upon which side does the triangle 3 seem to stand? Then _i j_ is called the _base_ of the triangle. What letter marks the vertex of the angle opposite the base? Then the point _g_ is said to be the vertex of the triangle. If, in the triangle 7, we consider _t v_ the base, what point is the vertex? If _v_ be considered the vertex, which side will be the base? In the triangle 3, what side is opposite the right angle? Then _g j_ is called the _hypothenuse_ of the triangle. _The hypothenuse of a triangle is the side opposite the right angle._ Read the hypothenuse of each of the triangles 5, 6, and 11. Either side about the right angle may be considered the base. Then the other side will be the perpendicular. In the triangle 3, if _i j_ is the base, which side is the perpendicular? If _g i_ be considered the base, which side is the perpendicular?