Download Geometry Name Cumulative Review Chapters 1 to 3 Due Date

Geometry
Cumulative Review Chapters 1 to 3
Name _______________________________
Due Date ________________ period _____
Chapter One
1. Given A (3, -9) and B (-6, 11).
a) Find AB, the distance between the two points.
b) Find the midpoint of ̅̅̅̅
𝐴𝐵 .
2. Given a segment with endpoint (-10, 5) and midpoint (4, -3). Find the coordinates of the other
endpoint.
3. A center pivot irrigation system uses a fixed water supply to water a circular region of a field.
The radius of the watering system is 560 feet long. Find the circumference and the area of the
watered region. Make a sketch.
4. Q is between P and R. PQ = 2w – 3, QR = 4 + w, and PR = 34. Find the value of w, PQ, and QR.
5. <A and <B are complementary angles. Given m<A is 4 times that of m<B. Find m<A and m<B.
6. Given m<A = 6xo, m<B = (19x + 5)o, and m<C = (5x + 13)o. Also given <A is acute, <B is the
supplement of <A and <C is the complement of <A. Find measures of <A, <B, and <C.
7. If ⃗⃗⃗⃗⃗
𝑄𝑆 bisects <PQR, find m<PQR given m<PQS = (5x – 46)o and m<SQR = (2x + 5)o. Make a
sketch.
8. Find the values of x and y.
9. Find the area of the shaded region below. (Use 3.14 for π)
Chapter Two
10. Given: If two points lie in a plane then the line containing them lies in the plane.
a) Write the converse of the above conditional statement.
b) If possible, write an appropriate true bi-conditional statement.
11. Given: A point is the midpoint of a segment if and only if it divides the segment into two
congruent segments.
a) Write the conditional statement for the given bi-conditional statement.
b) Write the converse of the given bi-conditional statement.
12. Write the converse of each of the following given statements. Determine if the converse is true
or false. If the converse is false, provide a counterexample.
a) If an angle measures 55o, then it is an acute angle.
b) If two angles measure 30o and 150o then the angles are supplementary.
c) If you chose the number 13 then you have chosen a prime number.
Chapter 3
13. Given: m ll n and m<1 = 34o. Find the measures of the remaining angles.
m
n
14. Use the diagram provided to answer each of the following.
a) List all pairs of corresponding angles
b) List all pairs of alternate interior angles.
c) List all pairs of alternate exterior angles.
d) List all pairs of consecutive interior angles.
15. Find the slope of the line containing (5, -8) and (9, 13).
16. Find the value of x in each of the following. a ll b in each of the diagrams below.
a)
b)
c)
17. Write each of the following equations in y = mx + b (slope-intercept) form. State the value of the
slope, m, and the value of the intercept, b, for each.
a) 3x – 8y = 24
b) 4y = -3x – 12
18. Write an equation of the line perpendicular to y = -2x + 4 that contains the point (-1, 2).
19. Write an equation of the line parallel to 3x – 4y = 12 that contains the point (3, -7).
20. Write the equation of the perpendicular bisector of the segment with endpoints (5, 5) and (1, 11).
Proofs
21. Write an algebraic proof to solve 9 – 3(2x + 3) = -11 + 5x for x.
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22. Given: <1≅ <2, and <3 ≅ <4
Prove: n ll p
23. Given: D is in the interior of <ABC
Prove: m<1 = m< ABC – m<2
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