Name
Date
35
Unit Test: Unit 7 Geometry
1. a) Describe each figure below.
b)
c)
i)
ii)
iii)
Choose pairs of figures. Say how they are alike and how they are different.
Identify:
an isosceles triangle with angle 50º
a parallelogram with side lengths 3 cm and 5 cm
a quadrilateral that is not regular
(10 marks)
Name
Date
Unit Test continued
2. Triangle PQR and ∆JKM have Q = K = 45 and PQ = JK = 5 cm.
(6 marks)
a) Which of the following measurements would ensure the triangles are congruent?
b) For each condition for congruent triangles, sketch the triangles and explain how you know
they are congruent.
i) QR = KM = 8 cm
ii) PR = JM = 4 cm
iii) P = J = 50
3. Use grid paper or dot paper.
a) Draw two octagons that have matching side lengths but different angles.
Are the octagons congruent? Explain.
b) Draw two octagons that have matching angles but different side lengths.
Are the octagons congruent? Explain.
c) Draw two congruent octagons with different orientations.
Explain how you know they are congruent.
(6 marks)
4. Describe the transformation for which
each of the figures A, B, and C
are the images of the shaded figure.
(3 marks)
5. Which of the following polygons can be used to tile the plane? Explain.
(3 marks)
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Date
Unit Test continued
6. a) Show how the trapezoid and the right triangle can be used to tile the plane.
Describe the tiling using transformations.
b) Explain how you can use transformations to describe each tiling.
(7 marks)
Name
Master 7.19
Date
Sample Answers
Unit Test – Master 7.18
1. a) Figure A is a parallelogram with 4 sides,
2 pairs of parallel sides, opposite sides equal, opposite angles equal, 2 obtuse angles, and 2 acute angles.
Figure B is a rhombus with 4 sides, all sides equal, opposite angles equal, and 2 pairs of parallel sides. Two angles are
acute and 2 angles are obtuse.
b)
c)
2. a)
b)
Figure C is a square with 4 sides, 2 pairs of parallel sides, all sides equal, and all right angles.
Figure D is an equilateral triangle with 3 equal sides and 3 equal acute angles. It is an acute triangle with each angle
measuring 60.
Figure E is an isosceles triangle with 3 sides,
2 equal sides, 2 equal angles, and 3 acute angles.
Figure F is a scalene triangle with 3 sides, no equal sides, and no equal angles. Each angle is an
acute angle.
Figure G is a rectangle with 4 sides, 2 pairs of parallel sides, opposite sides equal, and all right angles.
Figure B and Figure C both have 4 sides, with each side 3 cm. Figure B has 2 acute angles and 2 obtuse angles. Figure C
has all right angles.
Figure A and Figure G both have 4 sides, with
2 pairs of parallel sides and opposite sides equal. Figure A has 2 acute angles and 2 obtuse angles. Figure G has all right
angles.
Figure E and Figure F both have 3 sides, one angle of 50, and all acute angles. Figure E has
2 equal sides and 2 equal angles. Figure F has no equal sides and no equal angles.
i) Figure E
ii) Figure A
iii) Figures A, B, and G
i) iii)
i)
The triangles are congruent because 2 pairs of corresponding sides and the angle between them are equal: PQ = JK,
QR = KM, Q = K.
iii)
The triangles are congruent because 2 pairs of corresponding angles and the side between them are equal: PQ = JK,
P = J, Q = K.
3. a)
The octagons are not congruent because corresponding angles are not equal.
b)
The octagons are not congruent because corresponding sides are not equal.
c)
The octagons are congruent because corresponding sides are equal and corresponding angles are equal.
4. Rotate the shaded figure a
1
4
turn counterclockwise about its bottom left vertex to get Figure A.
Reflect the shaded figure in the vertical line through the point (7, 0) to get Figure B.
Translate the shaded figure 9 units right and 1 unit down to get Figure C.
5. The obtuse triangle can be used to tile the plane because all triangles tile the plane. The triangles can be arranged without
gaps, and at any point where vertices meet, the angles add to 360º.
The quadrilateral can be used to tile the plane because all quadrilaterals tile the plane. The quadrilaterals can be arranged
without gaps, and at any point where vertices meet, the angles add to 360º. The regular pentagon cannot be used to tile the
plane. A regular pentagon has 5 equal angles and each angle is 108º. Since 108 does not divide exactly into 360, I know that a
regular pentagon will not tile the plane. There will be gaps.
6. a)
b) Design 1: Translate the shaded trapezoid 4 units right to get trapezoid A. Reflect the shaded triangle in a vertical line through
the midpoint of the bottom side of the shaded trapezoid to get triangle D. Reflect triangle D in its right side to get triangle E.
Reflect triangle E in a vertical line through the midpoint of the bottom side of trapezoid A to get triangle F. Reflect the
section in a horizontal line through the bottom side of trapezoid A to get the next row. Continue reflecting to cover the page.
Design 2: Reflect the shaded trapezoid in a horizontal line 1 unit down from its bottom side to get trapezoid A. Reflect the
shaded triangle in a vertical line through the midpoint of the bottom side of the shaded trapezoid to get triangle B.
Translate the shaded triangle down
2 units to get triangle C. Rotate triangle C a
1
2
turn about the midpoint of its hypotenuse to get triangle D. Translate
triangles C and D 1 unit right to get triangles E and F. Translate triangles E and F
1 unit right to get triangles G and H. Translate triangles G and H 1 unit right to get triangles I and J. Reflect triangle C in
its bottom side to get triangle K. Translate triangle J down 2 units to get triangle L. Translate the section down 6 units to
get the next row. Continue translating to cover the page.