Integrated Algebra 1 Second Semester Final Review
Unit 4
The Distance Formula-
The Midpoint Formula-
1. Find the distance between the two points.
(-5, 3), (1, 2)
2. Find the midpoint of the line segment with the given endpoints. (-9,-5), (7, -14)
3. Describe a pattern in the numbers. Write the next number in the pattern.
1, 4, 9, 16,…
4. Show the conjecture is false by finding a counterexample.
The square root of a number x is always less than x.
5. For the given statement, write the if-then form, the converse, the inverse, and the contrapositive and indicate whether each statement is true or falst.
A regular pentagon has five sides.
6. Write the converse of the following statement and then write a biconditional statement.
If two angles are supplementary, then their sum is 180º.
Write the statement that follows from the given statements. Indicate whether the Law of Detachment of Law of Syllogism is used.
7. If Dr. Klein is well-rested for a surgical procedure, the she operates with precision. Dr. Klein got plenty of sleep to prepare for today’s operation.
8. If we don’t make any stops, then we’ll make it to the stadium by 12:30P.M. If we make it to the stadium by that time, then we should be in to time to see the kickoff.
Match the following statements with the congruence property being used.
____9. For any angle A, .A. Symmetric
____10. If , then .B. Reflexive
____11. If and , then C. Transitive
12. Complete the proof.
Given: AL=SK
Prove: AS=LK
Statments / Reasons1. AL=SK
2. LS=LS
3. AL+LS=SK+LS
4. AL+LS=AS
5. SK+LS=LK
6. AS=LK
13. If the measure of angle 1 is 53º, find the measure of angle 2, angle 3, angle 4, and angle 5.
14. Find the value of the variables and the measure of each angle in the diagram.
15.
16. RS is perpendicular to ST. Find the value of x.
17. List the five ways to prove triangles are congruent.
18. Use the given coordinates to determine if ΔABC ΔDEF.
A(1,2), B(4,-3), C(2,5), D(4,7), E(7,2), F(5,10)
Decide whether the congruence statement is true. Explain your reasoning. If it is true, state the congruence postulate or theorem that is used.
19. ΔABCΔEDC
20. ΔPQR ΔSTU
21. ΔMNP ΔPQM
22. Complete the Proof.
Given: B is the midpoint of.
B is the midpoint of.
Prove ΔABDΔEBC
Statements / Reasons1. B is the midpoint of . / 1.
2. / 2. Definition of midpoint
3. B is the midpoint of . / 3.
4. / 4. Definition of midpoint
5. <ABD<EBC / 5.
6. ΔABDΔEBC / 6.
Unit 5
23. Find the length of .
24. The point of concurrency of the perpendicular bisectors of a triangle is called the
______.
25. The point of concurrency of the angle bisectors of a triangle is called the ______.
26. The point of concurrency of the altitudes of a triangle is called the ______.
27. The point of concurrency of the medians of a triangle is called the ______.
28. Find the length of.
29. The perpendicular bisectors meet at point G and are shown dashed.
30. Find AD.
31. Point P is the incenter of ΔHKM. Find JP.
32. G is the centroid of ΔABC, AD=8, AG=10, and CD=18.
33. List the sides in order from least to greatest.
34. List the angles in order from least to greatest.
35. Is it possible to construct a triangle with the given side lengths? If not, explain why not. 10, 57, 45.
Complete the statement with <, >, or =. Tell whether you used the Hinge Theorem or the converse of the Hinge Theorem.
36.
37.
38. The sum of the measure of the interior angles of a convex n-gon is ______.
39. The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is ______.
40. Find the sum of the measures of the interior angles in a convex 15-gon.
41. The sum of the measures of the interior angles of a convex polygon is 2520º. Classify the polygon by the number of sides.
42. Find the measures of an interior angle and an exterior angle of a regular octagon.
43. Find the value of x.
44. Find the value of each variable in the parallelogram.
45. Find the value of each variable in the parallelogram.
For what value of x is the quadrilateral a parallelogram?
46.
47. Decide whether you are given enough information to determine that the quadrilateral is a parallelogram.
Opposite sides are parallel.
Two pairs of consecutive sides are congruent.
Diagonals are congruent.
Diagonals bisect each other.
Consecutive angles are supplementary.
All four sides are congruent.
48. Classify the quadrilateral. Explain your reasoning. Then find the values of x and y.
49. The diagonals of rhombus PQRS intersect at T. Given that m<RPS=30º and RT=6, find the indicated measure.
50. Find the value of x.
51. JKLM is a kite. Find the m<K.
52. Complete the chart. Put an X in the box if the shape always has the given property.
Property / Parallelogram / Rectangle / Rhombus / Square / Kite / Trapezoid1. Both pairs of opposite sides are congruent.
2. Both pairs of opposite angles are congruent.
3. Exactly one pair of opposite sides are congruent.
4. Exactly one pair of opposite sides are parallel.
5. Exactly one pair of opposite angles are congruent.
6. Consecutive angles are supplementary.