Download Year 10–10A Geometry Test (Foundation) Name: Class: Question 1

Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Multiple choice section – choose the correct answer
Question 1
Which one of the following statements is
false?
Question 5
ABC with
CDE can be
used as part of
a test for
congruency
because:
8.5
A A parallelogram has two pairs of
parallel sides.
B A square is a special type of rectangle.
C The diagonals of a rhombus bisect each
other at right angles.
D A kite has both pairs of opposite angles
equal.
Question 2
For triangles ABC and XYZ,
ABC  XYZ and ACB  XZY .
Which test for similarity can be used?
A SSS
B AAA C RHS
8.3
A they are alternate angles
B they are opposite angles
C their sum is 180º
D they are both acute angles
8.1
Question 6
The parallelogram will be
a rectangle if:
D SAS
Question 3
The value of x in the pair of similar
triangles is:
8.5
A opposite sides are parallel
B DAB  BCD
C DAB  BCD
D AC = BD
8.2
Question 7
For similar right-angled isosceles triangles
ABC and DEF , BAC  EDF  90 .
Which statement is true?
A 18
B 19
C 20
A ABC  DEF  90
AB DE

B
AC DF
C BC  EF
D EF is parallel to BC
D 21
Question 4
If ABC is congruent to DEF , which
statement is false?
8.3
Question 8
Similar triangles are:
A All matching sides are equal.
B ACB = 90°
C All matching angles are equal.
D All of the properties for similarity
apply.
Question
number
Answer
1
2
3
A
B
C
D
4
8.4
5
8.2
ACF and ADH
ADH and BCE
BCE and ACF
AFC and ACG
6
7
8
9
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
10
Total
1
Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 9
Which statement is true?
A If a triangle has two matching sides and
a matching angle equal, they are
congruent using the SAS test.
B If two triangles have the same area, they
are similar shapes.
C If two pairs of matching sides of a
triangle have the same length, they are
congruent.
D All equilateral triangles are similar
shapes.
8.2
Question 10
The quadrilateral will be kite shaped if:
A
B
C
D
8.5
AD  AB
ABC  BCD
ABC  ADC
BC  CD
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Short answer section
Question 11
Use words from the list below to complete the following sentences.
bisect
congruent
included angle
similar
definition
theorem
2
perpendicular bisector
perpendicular
(a) To __________ a line is to divide its length into two equal lengths.
(b) If two shapes are identical in shape but different in size , they are said to be
______________.
Question 12
Explain congruent shapes, using an example to help you.
2
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Question 13
Triangles ABC and XYZ are similar triangles.
(a) State in fraction form the dilation factor used to
obtain ABC from XYZ .
4
8.4
2
8.2
(b) Find the value of x.
Question 14
Explain why two equilateral triangles that have a side of equal length are congruent triangles.
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 15
(a) Why are the two triangles in the diagram similar?
3
8.4
5
8.2
(b) Find the length of x, a side on the large triangle.
(c) Find the length of y, a side of the small triangle.
Question 16
A rectangular garden of dimensions 2.4 m × 7 m has been expanded so that the width is now
3.6 m.
(a) If the old garden shape and the new shape are similar figures, what is the length of the
new garden?
(b) The garden will be enlarged again, with the new length being 17.5 m. What will be the
width of the garden now?
(c) What dilation factor has been applied to enlarge the original garden to its final size?
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 17
(a) Show that ABC and ADC are congruent.
4
8.2
8.5
3
8.1
3
8.2
(b) If ABC  90 , show that ABCD is a rectangle.
Question 18
The small triangles in the diagram are all equilateral.
(a) Name two different-sized triangles that are similar to ADG .
(b) Name two rhombuses that are congruent to ABFH.
(c) Name a shape that is congruent to BCEFHJ.
Question 19
The parallelogram ACEG has midpoints at B, D, F and H.
(a) List the triangles that are similar to ACD .
(b) Which shapes are congruent to ABJH?
(c) How many pairs of vertically opposite angles are there?
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 20
The line segment OC is the reflection of OA in the y-axis. AD and CB are perpendiculars to
the x-axis.
(a) Explain which test for congruency can be used to show that
OAD  OCB .
3
8.3
2
8.4
(b) Prove that the y-axis bisects AC.
Question 21
Prove that ABD  CDB .
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 22
ABCD is a trapezium and E is the midpoint of AD and AD = 2BC
(a) Prove that ABE  CEB .
4
8.4
3
8.2
(b) Prove that ECD  CEB .
(c) What statement can be made about the relationship of ABE to ECD ?
(d) Why is ABCE a parallelogram?
Question 23
A ladder rests on a 1.2 m wall with one end against a
tree at a height of 7 m above the ground and the other
end on the ground. If the wall is 0.4 m from the
bottom of the ladder, find the:
(a) horizontal distance of the base of the ladder from
the bottom of the tree
(b) distance of the tree from the wall.
Short answer total:_________/40
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Extended answer section
Question 24
A special type of quadrilateral is shown.
(a) What is the name of this type of quadrilateral?
5
8.3
3
8.3
(b) List the equal sides.
(c) Write equations for any equal angles.
(d) Imagine that the two diagonals are drawn in the figure. State whether or not they are
perpendicular, equal in length, and whether they bisect each other.
(e) These two diagonals divide the figure into four triangles. Are these triangles congruent?
Are they equal in area?
Question 25
ABEF is a parallelogram. C is the midpoint of BE.
(a) Prove that AB = DE.
(b) Hence, show that E is the midpoint of DF.
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10–10A Geometry Test (Foundation)
Name: _____________________
Class: _____
Question 26
In the diagram, AC = EC and AF = EF.
(a) Prove that AFC  EFC.
6
8.3
6
8.3
(b) Prove that CG bisects ACE.
(c) Prove that EDF  ABF .
Question 27
XYQ and PZQ are different sized equilateral triangles.
(a) Show that YQP  XQZ .
(b) Show that QPY  QZX .
(c) Hence, show that YP = XZ.
Extended answer total:_________/20
Copyright © Pearson Australia 2012 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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