Download a) See the second attach b) Two teams, one from tower A and

a) See the second attach
b) Two teams, one from tower A and another from tower B, start going straight from each
location following the 2 black lines. They will meet at the source of smoke.
c) Two ships A and B, on the sea could observe a light C at the shore. For ship A, the
light tower is situated at the bearing of 45 degrees (clockwise from North), while for ship
B, the light tower is situated 330 degrees (clockwise from North ).
The student is wrong. We could measure an angle because it doesn’t matter how long the
two rays are. We could put two points A and B on the two rays, and the angle doesn’t
change. The angle between the 2 rays is same as the angle AOB, which it could be
measured with a protractor.
In geometry, two figures are congruent if they have the same shape and size, but are in
different positions (for instance one may be rotated, flipped, or simply placed somewhere
else).
For example, two angles ABC and DFE, say, are "equal" if and only if there are exactly
the same angle: that would mean that B and F are just different ways of referring to the
same point and that A is on one of the rays FD or FE and C is on the other one.
Two angles are "congruent" if and only if they have the same measure.
Generally speaking, in mathematics, we use the term "equal" to mean "(possibly
different) ways of referring to exactly the same object" and "congruent" to mean "have
some specific property in common".
Geometry, as developed in Euclid, was a systematic body of mathematical knowledge,
built by deductive reasoning upon a foundation of three main pillars: (1) definitions of
such things as points, lines, planes, angles, circles, and triangles; (2) the assumption of
certain geometrical postulates regarded as true but perhaps not self-evident; and (3) the
assumption of certain axioms or common notions which were taken to be self-evident
truths. The body of Euclid's great work consists of a set of propositions or theorems, each
derived systematically and logically from the definitions, axioms, and postulates of his
foundation and from theorems already proved.
See the second attach
See the second attach
We’ll use the fact that, in any right triangle, the sum of the other two angles =90
Therefore, since triangle ACB is right, then 55 + B = 90, so B = 35 degrees.
Triangle CDB is also right, so x + B = 90. That makes x + 35 = 90.
So we conclude that x = 35 degrees.
The intersection between a plane and a cube could be:
a) a square
b) a rectangle
c) a triangle
The drawings are on the second attached
It has 8 lateral faces. Each lateral face corresponds to a base side.
The edges of the 2 base squares of the cube don’t look parallel as they do in a normal
square on a piece of paper, because since the two base- squares of the 3- dimensional
cube on a plane look like parallelograms. Compare those two pictures:
Cube in a plane (bases are in black)
Square in a plane (attached)
A cylinder need not have circular bases, nor must a cylinder form a closed surface. If
MNPQ is a curve in a plane (Fig. 1), and APB is a line that is not in the plane and that
intersects the curve at a point P, then all lines parallel to AB and intersecting MNQ
when taken together form a cylindrical surface. If the curve MNPQ is closed, the
volume enclosed is a cylindrical solid. The term cylinder may refer to either the solid
or the surface. The line APB, or any other line of the surface that is parallel to APB, is
called a generatrix or element of the cylinder, and the curve MNPQ is called a
directrix or base. In a closed cylinder, all the elements taken together form the
lateral surface. A closed cylinder is circular, elliptical, triangular, and so on, according
to whether its directrix is a circle, ellipse, or triangle. In a right cylinder, all elements
are perpendicular to the directrix; in an oblique cylinder, the elements are not
perpendicular to the directrix. In general, the volume of a closed cylinder between
the base and a plane parallel to it is given by Bh, in which B is the area of the base
and h is the perpendicular distance between the two parallel planes