Download Geometry Chapter 1 Review (Answer Key on Page 3) 1. Your friend

Geometry
Chapter 1 Review
(Answer Key on Page 3)
1. Your friend draws a square and one diagonal connecting its opposite vertices. Your friend believes that
the diagonal is the same length as one side of the square. Do you agree? Explain your reasoning.
2. Find the perimeter of quadrilateral PQRS with the vertices P2, 4, Q2, 3, R 2,  2, and S  2, 3.
3. A rectangle has vertices 1, 4, 3, 4, and 3, 3. Find the remaining vertex of the rectangle. What is the
area of the rectangle?
In Exercises 4 and 5, find the area of the polygon with the given vertices.
4. T 0,  2, U 3, 5, V 3, 5
5. A3, 3, B3, 1, C4, 1, D4, 3
In Exercises 6–10, use the diagram.
6. Find the perimeter of square ADEF.
7. Find the perimeter of ! BCD.
8. Find the area of square ADEF.
9. Find the area of ! ACD.
10. Find the area of pentagon ACDEF.
In 11-12, find the indicated angle measure.
11. mEFG  130. Find mHFG.
12. mJNM  103. Find mJNK.
In Exercises 13–15, use the figures.
13. Name a pair of adjacent complementary angles.
14. Name a pair of nonadjacent complementary angles.
15. Name a pair of nonadjacent supplementary angles.
In Exercises 16–18, write and solve an algebraic equation to find the measure of each angle based on the
given description.
16.Two angles form a linear pair. The measure of one angle is 24 more than the measure of the other angle.
17.The measure of an angle is three times the measurement of its complement.
18.The measure of one angle is 15 less than half the measurement of its supplement.
19. Find the measure of each angle.
ABC and CBD are supplementary angles, mABC  7 x and mCBD  8x.
In Exercises 20–21, use the figure.
20. Identify the linear pair(s) that include 2.
21. Are 6 and 8 vertical angles? Explain your reasoning.
22-25, use the diagram.
22. Give another name for line S.
23. Name three points that are coplanar.
24. Name three points that are collinear.
25. Give another name for plane K.
26. Plot the points in a coordinate plane. Then determine whether
AB and CD are congruent: A 2, 1, B2, 1, C 3, 2, D3,  2.
27. Plot the points on your own coordinate plane.
a. A1, 2, B1, 4, C6, 2,
b. D3, 4, E3, 6, F 8, 4
c. Find the area of each triangle. Do the triangles have the same area? Explain.
28. What is the midpoint of a segment with the following endpoints?
a. A(3, 6), B(10, 6)
b. C(1, 8), D(7, 2)
29-30, the midpoint of PQ is M. Calculate the missing coordinates.
29. P(9, –2), M(–3, 4) Q
30. Q(8, –1), M(4, 1) P
31-32, find the distance between each pair of points. Leave your answer in simplest radical form.
31. J(0, 5), Q(3, 9)
32. K(–6, 12), P(2, 7)
Answers:
1. No. Because the diagonal is also the hypotenuse of the right triangle, it must be longer than the other 2
legs.
2. ≈ 16.5 un
3. (1, – 3); 14 un2
4. 21 un2
5. 28 un2
6. 22.6 un
7. 10.5 un
8. 32 un2
9. 12 un2
10. 44 un2
11. 44°
12. 47°
13. FJG, GJH
14. CAD, EJF
15.
16.
x   x  24  180; 78 and 102
17. x  3x  90; 22.5 and 67.5
18.
x
19. mABC  84, mCBD  96
20. 1 and 2, 3 and 2
BAC, EJG
 12 x  15  180; 50 and 130
21. yes; The sides form two pairs of opposite rays.
22-25 are sample answers; there could be others
22. Sample answer: XR
23. Sample answer: points T, Q, and P
24. Sample answer: points T, R, and Y
25. Sample answer: plane TRP
26. AB  CD
27. a.
b. Each triangle has an area of 5 square units.
c. yes; They are congruent triangles.
13
28. a. ( 2 , 6)
b. (4, 5)
29. (– 15, 10)
30. (0, 3)
31. 5 un
32. √89 ≈ 9.43 un.