## Plane and Solid Geometry |

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Page 4

When two straight lines intersect so as to form

called a right angle , as EOD , DOF , etc. A right angle is half a straight angle . 32.

An acute angle is an angle less than a right angle , Ks G K as angle IKH H 33.

When two straight lines intersect so as to form

**four**equal angles , each angle iscalled a right angle , as EOD , DOF , etc. A right angle is half a straight angle . 32.

An acute angle is an angle less than a right angle , Ks G K as angle IKH H 33.

Page 6

What kind of an angle is less than its supplement ? equal to its supplement ?

greater than its supplement ? B 14.

point . Which angle is the sum of AOB and BOC ? the sum of BOC and COD ? the

...

What kind of an angle is less than its supplement ? equal to its supplement ?

greater than its supplement ? B 14.

**Four**lines , AO , BO , CO , and DO , meet in apoint . Which angle is the sum of AOB and BOC ? the sum of BOC and COD ? the

...

Page 11

A polygon of three sides is called a triangle ; one of

TRIANGLES 62. A triangle having three unequal sides is a scalene triangle . An

isosceles triangle has two of its sides equal . An equilateral triangle has its three

...

A polygon of three sides is called a triangle ; one of

**four**sides , a quadrilateral .TRIANGLES 62. A triangle having three unequal sides is a scalene triangle . An

isosceles triangle has two of its sides equal . An equilateral triangle has its three

...

Page 14

AC will coincide with A'C " . .. A ABC and A'B'C " coincide . .. A ABC = A A'B'C " .

Q.E.D. Ex . 35. If two lines bisect each other , and their extremities are joined ,

AC will coincide with A'C " . .. A ABC and A'B'C " coincide . .. A ABC = A A'B'C " .

Q.E.D. Ex . 35. If two lines bisect each other , and their extremities are joined ,

**four**triangles are formed , of which those opposite each other are equal . 73. Page 16

If

then ( 1 ) ZABE > LACE , ( 2 ) ZABE > < CED , ( 3 ) LABE > LADE . ( See diagram

on next page . ) Ex . 44. If in quadrilateral ABCD the diagonals AC 16 P̀ANE ...

If

**four**points , A , B , C , and D , in a straight line be joined to a point , E , without ,then ( 1 ) ZABE > LACE , ( 2 ) ZABE > < CED , ( 3 ) LABE > LADE . ( See diagram

on next page . ) Ex . 44. If in quadrilateral ABCD the diagonals AC 16 P̀ANE ...

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### Common terms and phrases

ABCD altitude angle angles are equal base bisect bisector called chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divide draw drawn equal equidistant equivalent exterior angle faces figure Find formed four geometrical given circle given line given point greater Hence homologous hypotenuse inches included inscribed intersecting isosceles triangle length less limit line joining measured median meet midpoints opposite sides parallel parallel lines parallelogram passing perimeter perpendicular plane polyedron polygon prism PROBLEM Proof PROPOSITION prove prove Hyp pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle School segments sides similar sphere spherical triangle square straight line surface tangent THEOREM third transform triangle triangle are equal vertex vertices

### Popular passages

Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.

Page 180 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.

Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...

Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.

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Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.