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
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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
Then a right angle is an angle of how many degrees?
If an angle stand upon less than 90°, what kind of an angle is it?
If an angle stand upon more than 90°, what kind of an angle is it?
Can an angle have as many degrees as a hundred and eighty?
LESSON THIRTY-FIFTH.
REVIEW.
Read nine arcs whose ends are marked. (DIAGRAM 26.)
Read three arcs each of which is one-fourth of a circumference.
Read two arcs each of which is one-half of a circumference.
Why is _e g_ an arc?
What is an arc?
How many degrees in the arc _f h_? In _e h_?
If the arc _f h_ were divided into three equal parts, how many degrees
would there be in each?
How many degrees in a circumference?
In a semi-circumference?
How many more degrees in a large circumference than in a small one?
If the arc _i f_ is 40°, what is the size of the angle _f o i_?
If the angle _f o g_ is an angle of 130°, what is the size of the arc
_f i h g_?
How many degrees in each of the adjacent angles _f o h_, _h o e_?
When two adjacent angles are equal to each other, what is each called?
How many degrees in a right angle?
[Illustration: Diagram 26.]
LESSON THIRTY-SIXTH.
PARTS OF THE CIRCLE.
The part of the circle bounded by the chord _a b_ and the arc _a b_ is
called a segment.
Read three segments, each less than half a circle, thus,—the segment
bounded by the chord _a d_ and the arc _a b d_.
_A segment is a part of a circle bounded by an arc and a chord._
Read two segments that are each half a circle.
What is the chord called?
What is the arc called?
A segment bounded by a diameter and a semi-circumference is a
“_semicircle_.”
_A semicircle is half a circle._
Read four segments each larger than a semicircle.
The part of the circle between the two radii _o f_, _o i_, and the arc
_f i_, is called a “_sector_.”
Read four sectors each less than one-fourth of a circle.[2]
Footnote 2:
Thus, a sector bounded by the two radii _o g_, _o h_, and the arc _g
h_.
_A sector is a part of a circle bounded by two radii and an arc._
What part of the whole circle is the sector _f o h_?
It is called a “_quadrant_.”
_A quadrant is a sector which is one-fourth of a circle._
Read a sector which is greater than a quadrant.
If the chord _e f_ be regarded a diameter, what do you call the
semicircle below it?
If it be regarded as two radii, what is the semicircle called?
Then a semicircle is both a segment and a sector.
LESSON THIRTY-SEVENTH.
REVIEW.
Name ten segments. (DIAGRAM 26.)
What is a segment?
Of the segments named, which are less than a semicircle?
Which are greater?
Which two are semicircles?
Which two are on the chord _a f_?
Name nine sectors.
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