Basic Geometry

Question 1

describe line (3 points)s

Answer 1

-a line l is formed if we extend a line segment A and B
-we use a small letter to label a line, eg line l
-a line has one dimension; it has an indefinite length but no breadth or thickness

Question 2

describe ray (2 points)

Answer 2

-a ray is a line with only one endpoint
-an example of a ray is a light from a source such as the Sun or a lamp

Question 3

describe plane (3 points)

Answer 3

-a plane is a flat two-dimensional surface: it has a length and a breadth, but no thickness
-it is made up if an infinite number of points
-the floor is an example of a horizontal plane and a wall is an example of a vertical plane

Question 4

What does it mean for three points to be collinear?

Answer 4

If we can draw a line to pass through three distinct points on a plane, then the three points lie on the same line

Question 5

What are intersecting lines?

Answer 5

If two lines on a plane intersect at one point X, they are called intersecting lines. The point X is known as the point of intersection.

Question 6

What are perpendicular lines?

Answer 6

If two intersecting lines intersect each other at right angles, they are called perpendicular lines. We write AB ⟂ PQ. F is known as the foot of the perpendicular from P to AB.

Question 7

What are parallel lines?

Answer 7

If two lines on a plane do not intersect at any point, they are called parallel lines. We write AB // CD.

Question 8

complementary angles meaning

Answer 8

two angles when they add up to 90°

Question 9

supplementary angles meaning

Answer 9

two angles when they add up to 180°

Question 10

3 factors that make an adjacent chamber

Answer 10

-share a common vertex
-have a common side
-lie on opposite sides of the common side

Question 11

how to show that the sum if adjacent angles on a straight line is 180°

Answer 11

adjacent angles on a straight line

Question 12

Answer 12

Question 13

how to show that the sum of angles at a point is 360°

Answer 13

angles at a point

Question 14

Answer 14

Question 15

how to show that vertically opposite angles are equal

Answer 15

vertically opposite angles

Question 16

Answer 16

Question 17

prove corresponding angles a and b

Answer 17

angle a = angle b (corresponding angles, PQ//RS)

Question 18

prove alternate angles c and d

Answer 18

angle c = angle d (alternate angles, PQ//RS)

Question 19

prove that PQ//RS using angle a and angle b

Answer 19

angle a = angle b, then PQ//RS (converse of corresponding angles)

Question 20

prove interior angles are supplementary

Answer 20

angle b + angle d = 180° (interior angles, PQ//RS)

Question 21

prove that angle c = angle d

Answer 21

if angle c = angle d, then PQ//RS (converse of alternate angles)

Question 22

prove that angle b + angle d = 180°

Answer 22

if angle b + angle d = 180°, then PQ//RS (converse of interior angles)

Question 23

In the figure, AB // CD. Calculate the values of a, b and c.

Answer 23

To find the value of c:
Method 1:
c° = angle BTS (corresponding angles, AB//CD)
= 61°

∴ c° = 61°

Method 2:
c° = 180° - b° (adjacent angles on a straight line)
= 180° - 119°
= 61°

∴ c = 61°

Question 24

Answer 24

Question 25

Answer 25

Question 26

Answer 26

complementary angles add up to 90°

Question 27

Answer 27

supplementary angles add up to 180°

Question 28

Answer 28

vertically opposite angles are equal

Question 29

Answer 29

sum of adjacent angles on a straight line = 180° (supplementary angles)

Question 30

Answer 30

sum of adjacent angles at a point = 360°

Question 31

Answer 31

Question 32

Answer 32

Question 33

Answer 33