Two pairs of alternate interior angles. Two pairs of alternate exterior angles. Why are the angles _i o m_, _m o j_, called adjacent? What are adjacent angles? What kind of an angle is _i o m_? Why? What is an acute angle? What kind of an angle is _m o j_? Why? What is an obtuse angle? Why are _a c f_, _f c b_, right angles? What is a right angle? Why are _m o i_, _j o p_, vertical angles? What are vertical angles? Why is _m o i_ an exterior angle? What is an exterior angle? Why is _j o p_ an interior angle? What is an interior angle? Why are _m o i_, _o p k_, opposite angles? What are opposite angles? Why are _j o p_, _o p k_, alternate angles? What are alternate angles? LESSON EIGHTEENTH. PROBLEMS. Draw an obtuse angle which shall be only a little larger than a right angle. Draw one which shall be much greater than a right angle. Draw an acute angle which shall be only a little less than a right angle. Draw one which shall be much less than a right angle. Draw an obtuse angle with lines about one inch long. Draw an acute angle with sides three inches long. Which is greater, the obtuse angle, or the acute angle? Draw a right angle with lines an inch long. Draw one with lines five inches long. Which is the greater, first or the second? [Illustration: Diagram 16.] LESSON NINETEENTH. POLYGONS. Name any thing besides your desk that has a flat surface. A flat surface is called a plane. How many sides has the plane Fig. A? (DIAGRAM 16.) It is called a triangle. “Tri” means “three.” What other triangles do you see. Triangles are sometimes called trigons. _A triangle is a plane figure having three sides._ How many sides has the plane figure marked B? How many angles? It is called a quadrangle, or quadrilateral. “Quad” denotes “four.” What other quadrangles do you see? Why is Fig. B a quadrangle? _A quadrangle is a plane figure having four sides._ How many sides has the Fig. C? It is called a _pentagon_. What other pentagon do you see? Why is Fig. C a pentagon? _A pentagon is a plane figure having five sides._ In like manner,— _A hexagon is a plane figure having six sides._ _A heptagon is a plane figure having seven sides._ An octagon has eight sides. A nonagon has nine sides. A decagon has ten sides. All these figures are called _polygons_. “Poly” means “many.” What do you call a polygon of three sides? Of four sides? Of six sides? &c. If the length of each side of triangle A is one inch, how long are the three sides together? The sum of the sides of a polygon is its perimeter. Which of the triangles has unequal sides? Which has equal sides? The latter is called a _regular polygon_.