Download smaller angle?

Name:
Common Core Geometry Review
1) If
2)
intersects
Date:
Mr. Modiano
at E, m<AEC = 3x, and m<AED = 5x - 60, find the value of x.
The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle?
3) In the diagram,
||
,m
x = 50, and m y = 60. What is m z?
4) Given ABC and DBF find x and y.
5) Given the regular hexagon, describe a rigid motion or sequence of rigid motions that would map
∆AOB onto ∆DOC.
6) What is the minimum rotation that would map the hexagon onto itself?
7) Jenna is walking around the outside of a building that is in the shape of a regular polygon. She determines
that the measure of one exterior angle of the building is 20°.
a) How many sides does the building have?
b) What is the sum of the interior angles in this polygon?
c) Why doesn’t Jenna have anything better to do?
8) A STOP sign is a regular octagon. What is the measure of an interior angle?
9) Triangle ABC is dilated with C as the center of dilation.
What is the scale factor that maps ABC onto A'B'C"?
10) Prove W = Y + Z (the exterior angle theorem).
11) In the accompanying diagram of a construction, what does
1.
2.
3.
4.
an altitude drawn to
a median drawn to
the bisector of ∠APB
the perpendicular bisector of
represent?
12) Given: AB CD and CB DE prove <b + <d = 1800
13) Construct an equilateral triangle using AB?
14) Construct a median from A to BC.
15) Construct a square in the given circle
16) Construct a line perpendicular to line l that passes through point P
17) The centroid of a triangle divides a median into a ratio of
(1) 5:4
(2) 6:3
(3) 2:1
(4) 3:2
18) The circumcenter is the point of concurrency for the __________________.
19) The orthocenter is the point of concurrency for the __________________.
20) The incenter is the point of concurrency for the __________________.
21) The centroid is the point of concurrency for the __________________.
22.) You are looking at a triangle where the orthocenter and circumcenter are outside of the triangle.
What type of triangle are you looking at?
(1) isosceles
(2) obtuse
(3) equilateral
(4) right
23) Which type of triangle would have its orthocenter on the triangle?
(1) right
(2) scalene
(3) obtuse
(4) equilateral
24) Which of the four centers always remains inside a triangle?
And
.
25) A centroid located on median AQ is 8cm away from the vertex A, how far is it from the midpoint Q?
1) 8cm
(2) 16cm
(3) 24cm
(4) 4cm
26) The given diagram shows the construction of parallel lines. Which statement justifies this construction?
(1) Since the angles were bisected the lines must be parallel
(2) Since the alternate interior angles are congruent, the lines must be parallel.
(3) Since the corresponding angles are congruent, the lines must be parallel.
(4) The perpendicular bisector creates parallel lines.
27) P is the centroid of triangle ABC, if CF = 18, find the measure of X.
Use the diagram to the right to answer questions 28 through 31
_____28) Find:
rk rm ( B)
_____29)Find
rk rm (GF )
_____30) Find
Rt ,90o rk D 
_____31) Find
Rt ,135o rk E 
_____32) Which letter has point symmetry but not line symmetry?
(1) H
(3) T
(2) S
(4) X
_____33) Which letter has both point and line symmetry?
(1) Z
(2) T
(3) C
(4) H
_____34) The image of point A(4,-5) under a translation is A’(3,-l). What is the image of point (4,2) under the
same translation?
(1) (3,-2)
(2) (9,-2)
(3) (0,7)
(4) (3,6)
_____35) What is the image (3.-5) after R900?
(1) (5,3)
(2) (-3,5)
(3) (-3,-5)
_____36) Which of the following is equivalent to
(1)
R240o
(2)
R40o
(3)
(4) (-5,-3)
R40o ?
R320o
(4)
R320o
37) Enlarge triangle ABC with C as the center of dilation and a scale factor of 3.
38) Determine the scale factor of the dilation pictured to the right.
39) The figure on the right has how many lines of symmetry?
(1) 3
(2) 6
(3) 9
(4) 12
40) How many different rotations including the identity map the given
figure onto itself? (Same figure as question 39)
(1) 3
(2) 6
(3) 9
(4) 12
41) A centroid located on median AQ is 8cm away from the vertex A, how far is it from the
midpoint Q?
1) 8cm
(2) 16cm
(3) 24cm
r
42) What is y = 3 (2,-5)?
(1) (-5,8)
(2) (5,-5)
(3) (1,-2)
43) How many lines of symmetry does
(1) 1
(2) 2
(3) 0
(4) (-1,2)
ABCD possess?
(4) 4
(4) 4cm