Mathematics Grade 9 1 Geometry

Mathematics

1

Geometry

Grade 9

Straight Lines

1. Study the diagrams and fill in the correct statement or appropriate reason.

a)

Statement: 1 + 2 = 180?

Reason: ____________________________ ____________________________

b)

Statement: ________________________ Reason: exterior angle of a triangle equals the sum of the two opposite interior angles

c)

In right angled triangle ABC:

Statement:

2 = ____________________________ 2 = ____________________________

Reason: Pythagoras

2. Name the type of triangle or quadrilateral according to the information given.

Diagram a)

Name

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b)

Grade 9

c)

d)

e) > 90?

3. Determine the value of , and , in alphabetical order, for each diagram. All reasons must be given.

a)

Statement

Reason

50?

b)

38?

Statement

Reason

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c) The quadrilateral below is a parallelogram.

3 Statement

Reason

d) The quadrilateral below is a square.

Statement

Reason

Grade 9

e)

Statement

Reason

f) The quadrilateral below is a rhombus

50?

Statement

Reason

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Grade 9

4. Determine the value of , , , and , in alphabetical order, for each diagram. All reasons must be given.

a)

Q

U

80?

a

S c

b

120?

V

R

T

Statement

Reason

b)

U

Statement

P

Q b

35? e

Rd V

X

T

a

c

Y S W

Reason

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5. In the rhombus below, determine 1 with reasons.

L

M

Statement

50? K

2 1

N Reason

Grade 9

6. Determine the value of 2.

D

F

2 1

80? E

Statement

100?

A

20?

B

C

Reason

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7. You are given the following information regarding the diagram below:

;

= 30? ;

= 50?

P

Q

R

Grade 9

S

T

Calculate, giving reasons, the size of . (Hint: Construct a line through parallel to )

Statement

Reason

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MEMO:

1. Study the diagrams and fill in the correct statement or appropriate reason.

a) Statement: 1 + 2 = 180?

Reason: 's on a str. line

b) Statement: 2 = +

Reason: exterior angle of a triangle equals the sum of the two opposite interior angles

Grade 9

c)

In right angled triangle ABC:

Statement: 2 = 2 + 2 2 = 2 - 2

Reason: Pythagoras

2. Name the type of triangle or quadrilateral according to the information given.

Diagram a) b) c) d) e)

Equilateral Triangle Obtuse angled triangle Scalene Triangle Kite Rhombus

Name

3. Determine the value of , and , in alphabetical order, for each diagram. All reasons must be given.

a)

50?

Statement = 50? = 130?

Reason Vert. opp. 's 's on a str. line

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38?

8 Statement = 52? = 52?

c) The quadrilateral below is a parallelogram.

Statement = 70? = 70?

Reason

Grade 9

Int. 's of a

Alt. 's ; parallel lines

Reason

Opp. 's of a parm. is =

Corr. 's ; opp. sides of parm. is parallel (opp sides of parm. is ||)

d) The quadrilateral below is a square.

y x

e)

f)

50?

Statement = 90? = 45?

Reason Diag. of a sqr. bisects perpendicularly Diag. of a sqr. bisects the corners

Statement

Reason

=

180?-48? 2

=

66?

Int. 's of a ; 's opp. = sides

= 180? - 66? - 90? = 24? Co-int. 's ; parallel lines

2 = 122 + 52 = 169 = 13 Pythag.

Statement = 50? = 50?

= 90?

Reason Diag. of rhom. bisect corners Opp. 's of rhom are = Diag. of rhom. bisect each other perpendicularly

4. Determine the value of , , , and , in alphabetical order, for each diagram. All reasons must be given.

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