Principles of Geometry
Name ________________________________
Period _________
Chapter 1 Review Guide
1. What are the three steps of inductive reasoning?
a. Step 1:
b. Step 2:
c. Step 3:
2. Find the next term in each sequence.
a. 2, 4, 8, 16, 32, __________
b.
7 7
7
7
, , , , __________
5 25 125 625
3. Draw the next shape in each pattern.
a.
b.
4. Use the diagram below to answer the following questions.
a. Name the plane parallel to plane RSC.
___________________________________________
b. Name four lines skew to ⃡𝑇𝐷.
___________________________________________
⃡ .
c. Name 3 lines parallel to 𝑇𝐷
___________________________________________
d. Name a point that is coplanar with T, S, and C.
___________________________________________
5. Name three points that are collinear in the following figure.
c. 3, 4, 7, 11, 18, __________
d. 4, 5, 8, 13, 20, __________
Principles of Geometry
Use the diagram to the right to answer the following questions.
6. Name 𝐷𝐹 another way. __________________
7. Name the ray that is opposite 𝐸𝐹 . _________________
Use the diagram to the right to answer the following questions.
8. Name ∠1 another way. _________________________________
9. Name ∠2 another way. _________________________________
Use a protractor to measure the following angles. Classify each angle as acute, obtuse, right or straight.
10.
11.
Classify each of the following angles as acute, obtuse, right or straight based on each of their measures.
12. 90° ________________________________
14. 93.5° _______________________________
13. 39° ________________________________
15. 180° _______________________________
16. If 𝑚∠𝐷𝑂𝐸 = 23° and 𝑚∠𝐶𝑂𝐷 = 20°, then
what is the measure of ∠𝐶𝑂𝐸?
17. Find the lengths x and y.
Sketch and label each of the following.
18. ∠𝐶𝐴𝑅 with its angle bisector 𝐴𝑇
19. Complementary angles ∠𝐴𝑅𝑇 and ∠𝐺𝑌𝑀
where 𝑚∠𝐺𝑌𝑀 = 25°.
Principles of Geometry
20. Supplementary angles ∠𝑅𝑈𝑁 and ∠𝐻𝐼𝑇
where 𝑚∠𝑅𝑈𝑁 = 25°.
21. Vertical angles ∠𝐿𝑈𝑉 and ∠𝐹𝑈𝑅
24. Isosceles right ∆𝐴𝐵𝐶 with 𝐴𝐵 = 𝐵𝐶
25. Scalene ∆𝑃𝑇𝑆 with 𝑃𝑆 = 3, 𝑆𝑇 = 5, 𝑃𝑇 =
7, and median ̅̅̅̅
𝑆𝑂
22. Linear pair ∠𝐻𝐴𝑇 and ∠𝑇𝐴𝑅
̅̅̅̅ parallel
26. Hexagon 𝑅𝐸𝐺𝐼𝑁𝐴 with diagonal 𝐴𝐺
̅̅̅̅ and 𝑁𝐼
̅̅̅̅
to sides 𝑅𝐸
̅̅̅̅ ∥ ̅̅̅̅
̅̅̅̅ ⊥ ̅̅̅̅
23. Trapezoid TRAP with 𝑇𝑅
𝐴𝑃 and 𝑇𝑅
𝐴𝑅
̅̅̅̅ the non27. Trapezoid TRAP with ̅̅̅̅
𝐴𝑅 and 𝑃𝑇
̅̅̅̅
parallel sides. Let 𝐸 be the midpoint of 𝑃𝑇
̅̅̅̅. Draw 𝐸𝑌
̅̅̅̅.
and 𝑌 be the midpoint of 𝐴𝑅
Translate each problem into a diagram. Then solve.
28. At one point in a race, Ringo was 15 feet behind Paul and 18 feet ahead of John. John was trailing
George by 30 feet. Paul was ahead of George by how many feet?
29. Edith is a TV cameraperson; Stella is a textbook editor; Janet is a ceramic artist; and Mary is an auto
mechanic. The editor has a higher income than Mary. The artist earns less than the mechanic. Edith
earns more than the mechanic but less than Stella. Who earns the most?
Principles of Geometry
Chapter 1 Skills Checklist
1.1 Patterns and Inductive Reasoning
□ I can define inductive reasoning, as well as identify good and bad uses of inductive reasoning.
□ I can use inductive reasoning to find the next term in a number pattern.
□ I can use inductive reasoning to find the next term in a picture pattern.
1.2 Points, Lines and Planes
□ I can identify and name points, lines, and planes.
□ I can define and identify collinear and coplanar points.
1.3 Segments, Rays, Parallel Lines and Planes
□ I can identify and name segments.
□ I can identify and name rays.
□ I can identify and name opposite rays.
□ I can define and name parallel lines and skew lines.
□ I can define and name parallel planes.
1.4 Measuring Segments and Angles
□ I can name an angle in three ways.
□ I can measure an angle using a protractor.
□ I can mark and identify congruent segments and congruent angles.
□ I can mark/label a diagram with given information.
□ I can identify given information by using a labeled diagram.
1.5 Writing a Good Definition
□ I can define, identify, and sketch/label a right angle, acute angle, obtuse angle, straight angle, midpoint
and angle bisector.
1.6 Defining Line and Angle Relationships
□ I can define, identify, and sketch/label perpendicular lines, pair of complementary angles, pair of
supplementary angles, pair of vertical angles, and a linear pair of angles.
1.7 Defining Polygons
□ I can classify, name, define, and sketch/label polygons and diagonals of polygons.
1.8 Defining Triangles
□ I can identify and sketch/label types of triangles.
1.9 Defining Special Quadrilaterals
□ I can identify and sketch/label types of triangles.
1.10 Translating Word Problems into Diagrams
□ I can translate a word problem into a diagram and solve the problem.