Problem 1 :
Look at the figure given below and answer the questions.
(i) Name three points that are collinear.
(ii) name four points that are coplanar.
(iii) Name three points that are not collinear.
Problem 2 :
Sketch the next figure in the pattern.
Problem 3 :
Use the map to find the distances between the three cities that lie on a line.
Problem 4 :
Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°.
Find the angle of vision seen by the left eye alone.
Problem 5 :
Find the coordinates of the midpoint of AB with endpoints A(-2, 3) and B(5, -2).
Problem 6 :
In the diagram shown below, RQ bisects ∠PRS. The measures of the two congruent angles are (x + 40)° and (3x - 20)°. Solve for "x".
1. Answer :
Part (i) :
Points D, E and F lie on the same line. So they are collinear.
Part (ii) :
Points D, E, F and G lie on the same plane. So they are coplanar. D, E, F and H are coplanar, even though the plane containing them is not drawn.
Part (iii) :
There are many correct answers. For instance, points H, E and G do not lie on the same line.
2. Answer :
Each figure in the pattern looks like the previous figure with another row of squares added to the bottom. Each figure looks like a stairway.
So, the sixth figure in the pattern must have six squares in the bottom row.
3. Answer :
Using the scale on the map, we can estimate that the difference between Athens and Macon is
AM = 80 miles
The distance between Macon and Albany is
MB = 90 miles
It has been explained in the picture given below.
Knowing that Athens, Macon and Albany lie on the same line, we can use the Segment Addition Postulate to conclude that the distance between Athens and Albany is
AB = AM + MB
AB = 80 + 90
AB = 170 miles
It has been explained in the picture given below.
4. Answer :
We can use the angle addition postulate.
m∠2 + m∠3 = 100° (The total for left eye is 100°)
m∠3 = 100° - m∠2 (Subtract m∠2 from each side)
m∠3 = 100° - 60° (Substitute 60° for m∠2)
m∠3 = 40° (Subtract)
Hence, the vision for the left eye alone measures is 40°.
5. Answer :
Use the midpoint formula.
Here,
(x_{1}, y_{1}) = A(-2, 3)
(x_{2}, y_{2}) = B(5, -2)
Then, the midpoint of AB is
= [(-2 + 5)/2, (3 - 2)/2]
= (3/2, 1/2)
It has been illustrated in the picture given below.
6. Answer :
Congruent angles have equal measures.
m∠PRQ = m∠QRS
Substitute given measures.
(x + 40)° = (3x - 20)°
Add 20° to each side.
x + 60 = 3x
Subtract x from each side.
60 = 2x
Divide each side by 2.
30 = x
So, x = 30. We can check by substituting to see that each of the congruent angles has a measure of 70°.
(i) Patterns and inductive reasoning worksheet
(ii) Points, lines and planes worksheet
(iii) Segments and their measures worksheet
(iv) Angles and their measures worksheet
(v) Segment and angle bisectors worksheet
(vi) Angle pair relationship worksheet
(vii) Perimeter, area and circumference worksheet
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