Download ACT Review Day 2 Notes Name: Algebra 2 Period: ______

ACT Review Day 2 Notes
Algebra 2
Name: _____________________________
Period: __________
Congruence: Two geometric figures are congruent if they have the same size and shape.
Similar: Two geometric figures are similar if they have different sizes but the same shape.
 All corresponding angles are congruent and all sides proportional.
Typical ACT Problems:
1. Two similar triangles have perimeters in the ratio of 5 : 6 . The sides of the larger triangle
measure 12in, 7in, and 5in . What is the perimeter, in inches, of the smaller triangle?
A.
B.
C.
D.
E.
18
20
22
24
32
2. Line segments GH, JK, and LM are parallel and intersect line segments FL and FM as shown in
the figure below. The ratio of the perimeters of FJK to the perimeter of FLM is 3 : 5 , and the
ratio of FH to FM is 1: 5 . What is the ratio of GJ to FG ?
A.
B.
C.
D.
E.
1: 5
1: 3
1: 2
2 :1
5:3
3. In the figure below, D is a point on AB and E is a point on BC such that DE AC . If DB  4
units long, AB  10 units long, and BC  20 units long, how many units long is EC ?
A.
B.
C.
D.
E.
4
6
8
10
12
Vertical Angles: Non-adjacent angles formed by a pair of intersecting lines.
Complementary Angles: A pair of angles whose measures add up to 90 degrees.
Supplementary Angles: A pair of angles whose measures add up to 180 degrees.
4. The three lines below intersect at a point
as shown. What is the measure of x?
5. What is the measure of the missing angles?
Typical ACT Problem:
6. In the figure below, F, G, H, and J are collinear. FG, GK, and HK are line segments of equivalent
length, and the measure of JHK is 120 . What is the degree of GFK ?
A.
B.
C.
D.
E.
30
45
60
120
150
Angle Sum of Polygons: If a convex polygon has n sides, then its interior angle sum is given by the
following equation: S  (n  2) 180 .
Typical ACT Problems:
7. In pentagon ABCDE, shown below, A measures 50 . What is the total measure of the other 4
interior angles?
A. 130
B. 200
C. 310
D. 432
E.
490
8. Given the triangle shown below with exterior angles that measure x, y, and z as shown, what
is the sum of x, y, and z?
A.
B.
C.
D.
E.
180
231
309
360
Cannot be determined from the given information
Angle Relationships of Parallel Lines
In the diagram below, two parallel lines are cut by a transversal line. Find all the angles that are
congruent and tell why.
9.
Typical ACT Problem:
10. Given parallel lines l and m, which of the following choices lists a pair of angles that must be
congruent?
A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 2 and 5
E. 3 and 5
 x  x 2 y1  y 2 
Midpoint Formula:  1
,

2 
 2
Distance Formula:
x
 x1    y 2  y1 
2
2
2
11. A graphing program draws a line segment on a computer screen so that its ends are at  5,2 
and  7, 8  . What are the coordinates of its midpoint?
12. Find the distance between P  1, 4  and Q  2, 3  . Give an exact value.
Typical ACT Problems:
13. The endpoints of the diameter of a circle O are A and C. In the standard  x, y  coordinate
plane, A is at  4, 3 and C is at  9,  2  . What is the y-coordinate of the center of the
circle?
A. 5
5
B.
2
1
C.
2
D. 1
E. 2
14. On a sonar map in the standard  x, y  coordinate plane, the Yellow Submarine and the
Sandwich Submarine are located at the points  7, 4  and  2, 6  , respectively. Each unit on
the map represents an actual distance of 5 nautical miles. Which of the following is closest to
the distance, in nautical miles, between the two submarines?
A.
B.
C.
D.
E.
5
19
27
30
67
15. Two girls walk home from school. Starting from school, Susan walks north 2 blocks and then
west 8 blocks, while Cindy walks east 3 blocks and then south one block. Approximately how
many blocks apart are the girls’ home?
A.
B.
C.
D.
E.
7.1
10.4
11.4
12.7
16.0
Circles, Central Angles, Inscribed Angles Etc.
1
measure of
2
Degree measure of central angle = degree
Measure of inscribed angle =
measure of intercepted arc
intercepted arc (if the vertex touches the circle).
A
30°
A
B
mAB  30
35°
B
mAB  2 35  70
16. Find the measures of the indicated angles. Assume diameter drawn.
16. _________
________
________
________
Typical ACT Problems:
17. In the figure below, if AOC is a central angle and equals 70 , what is the measure of ABC ?
A. 30
B. 35
C. 50
D. 70
E. 140
18. In the circle shown below, M is the center and lies on RU and ST . Which of the following is
NOT true?
A.
TUM measures 65
B.
TU is parallel to RS
C.
TXU measures 50
D.
E.
RM  TM
RS  SM
Standard Form of the Equation of a Circle:
 x  h   y  k 
2
2
 r2
Typical ACT Problem:
19. In the standard  x, y  coordinate plane, the center of the circle shown below lies on the x-axis
at x  4 . If the circle is tangent to the y-axis, which of the following is an equation of the circle?
A.
B.
C.
D.
E.
x  4  y
 x  4  y
x  4  y
x  4  y
x  y  4
2
2
2
4
2
2
 16
2
2
 16
2
2
4
2
 16
Random Typical ACT Problems:
20. In XYZ , Y is a right angle and Z measures less than 52 . Which of the following phrases
best describes the measure of X ?
A.
B.
C.
D.
E.
Greater than 38
Equal to 38
Equal to 45
Equal to 142
Less than 38