Download Geometry Unit 1 Review (sections 6.1 – 6.7)

Geometry
Unit 1 Review (sections 6.1 – 6.7)
1A, B: Slope, Distance, Parallel and Perpendicular
A
1. Find the slope of AB.
2. Find the slope of a line that is perpendicular to AB.
B
3. Find the distance between A and B (the length of AB. )
4. Write the equation of the line that is the perpendicular bisector
of AB.
1C: Performing Transformations
Using the diagram above to match the Image/Pre-Image listed on the left with the transformation listed on
the right.
Shape II
Shape I
5. Pre-image: Shape I
Image: Shape II
a. Rotated 180° around
the point (0 , 0)
6. Pre-image: Shape II
Image: Shape III
b. Reflected over the line
𝑦 = −𝑥
7. Pre-image: Shape IV
Image: Shape II
c. Rotated 270° counterclockwise around the
point (0 , 0)
8. Pre-image: Shape I
Image: Shape IV
Shape IV
Shape III
9. Pre-image: Shape I
Image: Shape III
Perform the requested transformations. Make sure to label A' and B’.
10. Reflect over the line y = -2.
d. Reflected over the line
𝑦=0
e. Rotated 90° counterclockwise around the
point (0 , 0)
11. Rotate 180° around the point (-1 , 2).
A
B
A
B
12. Reflect over the line 𝑦 = 𝑥.
13. Draw the line of reflection that maps P
onto P’. Then write its equation.
A
B
15.
14.
C
D
B
A
A'
B'
D'
C'
K
J
K'
I
I'
J'
1E: Rotational and Line Symmetry in Polygons
16. How many total diagonals are there on the regular polygon to
the left?
17. How many lines of symmetry are there on the shape
to the left?
18. List all of the degrees of rotational symmetry for the
shape to the left.
19. Is there any pattern between the number of sides of a polygon and the number of diagonals it has?
Explain or give an example.
1F: Quadrilaterals and their properties
20. Sketch and label rectangle ABCD in the space
below. Then mark your picture to indicate the
property that OPPOSITE SIDES ARE Parallel.
21. Sketch a quadrilateral whose diagonals are
perpendicular. MARK YOUR PICTURE to
indicate this property. Then give the most
specific name of the figure.
22. The rhombus has 2 lines of symmetry that
are also the diagonals of the figure.
EXPLAIN how a line of symmetry helps
prove that the DIAGONALS OF A RHOMBUS
BISECT EACH OTHER..
23. Sketch and label parallelogram ABCD in the
space below. Then mark your picture to
indicate the property that OPPOSITE ANGLES
ARE CONGRUENT.
24. Which of the following statements are
TRUE about the square?
Circle all that apply.
25. List the name(s) of all quadrilaterals that
share both of the following characteristics.




Diagonals are congruent.
Opposite sides are parallel.
Opposite angles are congruent.
The square is a rectangle.
26. The graph below shows the diagonal of a
square. Locate the other two vertices of the
square. Then use slope to verify that the figure
has 4 right angles.


Opposite sides are parallel.
The diagonals bisect the opposite angles.
Then support your reasoning using
symmetry of the figure.
27. Three vertices of a parallelogram are given
below. Identify the fourth vertex. Then use
slopes and distance to verify that the opposite
sides of a parallelogram and congruent and
parallel.