Marks' first lessons in geometry: In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.Marks, Bernhard
Science
Marks' first lessons in geometry: In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.
Marks, Bernhard
Geometry -- Study and teaching
Read the opposite interior angles on the same side.
Are the opposite angles _e m a_, _m n c_, both exterior or interior?
Then they are _opposite exterior and interior angles_.
Read two pairs of opposite exterior and interior angles on the right
of _e f_. On the left.
ALTERNATE ANGLES.
Do the angles _b m n_, _m n c_, lie on the same side of the
intersecting line _e f_?
Are they adjacent to each other?
Are they vertical angles?
Then they are alternate angles.
_Alternate angles lie on different sides of the intersecting line,
and are neither adjacent nor vertical._
Are the alternate angles _b m n_, _m n c_, exterior or interior?
Then they are called “_interior alternate angles_.”
Read another pair of interior alternate angles between _a b_ and _c
d_.
Are the angles _e m b_, _c n f_, alternate angles? Why?
Are they exterior or interior?
Then what may they be called?
Read another pair of exterior alternate angles.
Why are _e m a_, _d n f_, alternate angles? Why exterior alternate?
LESSON SIXTEENTH.
REVIEW.
Read the exterior opposite angles on the right of the line _e f_.
(DIAGRAM 14.)
On the left. On the right of _r s_. On the left.
Why are _e m a_, _c n f_, exterior angles?
Why are they opposite angles?
What are opposite angles?
Read the interior opposite angles on the right of the intersecting
line _e f_.
On the left of it. On the right of _r s_. On the left.
Read the interior alternate angles formed by the lines _a b_, _c d_,
and _e f_.
Which pair are acute angles?
Which pair are obtuse angles?
Why are _b m n_, _m n c_, interior angles? Why alternate? What are
alternate angles?
Read the exterior alternate angles of the same lines.
Read the acute interior alternate angles of the parallels _t u_, _v
w_. The obtuse.
The acute exterior alternate angles. Obtuse.
Read the pair of opposite exterior angles on the right of the line _e
f_. On the left.
On the right of _r s_. On the left.
[Illustration: Diagram 15.]
LESSON SEVENTEENTH.
REVIEW.
Read thirteen or more angles whose vertices are at _c_. (DIAGRAM 15.)
Read four obtuse angles.
Read two right angles.
What three acute angles equal one right angle?
Which is greater, the right angle 4, or the right angle 5?
The obtuse angle 6, or the acute angle 7?
Read twelve pairs of adjacent angles formed by the lines _w x_, &c.
Read six pairs of vertical angles formed by the same lines.
Read all the interior angles formed by the lines _i j_, _k l_, and _m
n_.
Read all the exterior angles formed by the same lines.
Two pairs of opposite exterior angles.
Two pairs of opposite interior angles.
Four pairs of opposite exterior and interior angles.
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