Student Name: Tools of Geometry Module Review
Student Name: Tools of Geometry Module Review Answer each of the following problems. Make sure to show your work. Notation 1. Given the plane DGF in the diagram, which points are collinear?
2. Which point is coplanar with A, B, and C in the diagram below?
3. In the diagram below, which two rays are opposite one another?
4. Why is the straightedge of a ruler not the same as a line?
Patterns and Conjectures 5. Predict the next number in the sequence: 1, 4, 16, 64…
Student Name: Tools of Geometry Module Review
6. Make a conjecture about the sum of primes based on the following pattern: 4=2+2 6=3+3 8=3+5 10 = 3 + 7 12 = 5 + 7 and so on.
7. The next number in the sequence -5, -2, 4, 13 is 25. Is this conjecture true or false?
8. What role do conjectures and counterexamples play in the process of finding a pattern?
Definitions and Postulates 9. If EG = 17 and FG = 12, use the segment addition postulate to find the length of segment EF.
Student Name: Tools of Geometry Module Review 10. What is a postulate?
11. What types of statements can be used as reasons in proofs?
12. Using the segment addition postulate, find the value of x if AB = 3x + 8 BC = 4x + 6 AC = 28
Student Name: Tools of Geometry Module Review Basic Geometric Shapes 13. Name the types of quadrilaterals and polygons in the picture.
14. What is another name for an equilateral quadrilateral?
15. The planet Mercury has a diameter of 4,878 km, whereas the Moon has a radius of 1736.5 km. Which object is larger and why?
16. When is a rhombus a rectangle? When is a rectangle is not a rhombus?
Student Name: Tools of Geometry Module Review Congruent Objects and Shapes 17. How many pairs of angles are congruent in the figures below?
18. What is the geometric definition for similar objects?
19. If two polygons are similar, must they also be congruent? Explain your answer.
20. Are the sides and angles of a rectangle congruent to each other? Explain.
Student Name: Tools of Geometry Module Review Perimeter, Circumference and Area 21. This pizza’s border is stuffed with cheese. How many inches around is the border if the diameter of the pizza is 8 inches?
22. What is the area of the grey matting in this 16” by 20” picture frame if the picture to be framed is 8” x 10”?
23. If the carpet in this den is 4’ by 6’, what is its perimeter?
Student Name: Tools of Geometry Module Review
24. How is the area of a rectangle related to the area of a triangle?
Introduction to Transformations 25. How was the purple triangle transformed into the orange triangle?
Student Name: Tools of Geometry Module Review 26. What type of transformation is illustrated in the picture below?
27. What type of transformation does the image below depict?
28. How is a reflection different than a rotation?
Geometric Constructions 29. A ______________ divides a segment or angle in half.
Student Name: Tools of Geometry Module Review 30. A line that intersects a segment at right angles while dividing the segment in half is called a ________.
31. How does a geometric construction differ from a drawing?
32. Is it possible to have a bisector that is not perpendicular to the segment that it bisects? Explain.
Congruent Constructions 33. The picture represents a final step used in...
34. ___________________ lines intersect at a right angle.
Student Name: Tools of Geometry Module Review 35. Explain how protractors are used in geometric constructions.
36. What is a segment bisector? Explain.
Reasoning through Logic Puzzles 37. Which symbol represents "or" in a truth table?
38. If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q, identifying which variable represents which statement. Then write this statement in symbolic form.
39. If the puppy is tired, then he will sleep. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.
40. Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2?
2. Which point is coplanar with A, B, and C in the diagram below?
3. In the diagram below, which two rays are opposite one another?
4. Why is the straightedge of a ruler not the same as a line?
Patterns and Conjectures 5. Predict the next number in the sequence: 1, 4, 16, 64…
Student Name: Tools of Geometry Module Review
6. Make a conjecture about the sum of primes based on the following pattern: 4=2+2 6=3+3 8=3+5 10 = 3 + 7 12 = 5 + 7 and so on.
7. The next number in the sequence -5, -2, 4, 13 is 25. Is this conjecture true or false?
8. What role do conjectures and counterexamples play in the process of finding a pattern?
Definitions and Postulates 9. If EG = 17 and FG = 12, use the segment addition postulate to find the length of segment EF.
Student Name: Tools of Geometry Module Review 10. What is a postulate?
11. What types of statements can be used as reasons in proofs?
12. Using the segment addition postulate, find the value of x if AB = 3x + 8 BC = 4x + 6 AC = 28
Student Name: Tools of Geometry Module Review Basic Geometric Shapes 13. Name the types of quadrilaterals and polygons in the picture.
14. What is another name for an equilateral quadrilateral?
15. The planet Mercury has a diameter of 4,878 km, whereas the Moon has a radius of 1736.5 km. Which object is larger and why?
16. When is a rhombus a rectangle? When is a rectangle is not a rhombus?
Student Name: Tools of Geometry Module Review Congruent Objects and Shapes 17. How many pairs of angles are congruent in the figures below?
18. What is the geometric definition for similar objects?
19. If two polygons are similar, must they also be congruent? Explain your answer.
20. Are the sides and angles of a rectangle congruent to each other? Explain.
Student Name: Tools of Geometry Module Review Perimeter, Circumference and Area 21. This pizza’s border is stuffed with cheese. How many inches around is the border if the diameter of the pizza is 8 inches?
22. What is the area of the grey matting in this 16” by 20” picture frame if the picture to be framed is 8” x 10”?
23. If the carpet in this den is 4’ by 6’, what is its perimeter?
Student Name: Tools of Geometry Module Review
24. How is the area of a rectangle related to the area of a triangle?
Introduction to Transformations 25. How was the purple triangle transformed into the orange triangle?
Student Name: Tools of Geometry Module Review 26. What type of transformation is illustrated in the picture below?
27. What type of transformation does the image below depict?
28. How is a reflection different than a rotation?
Geometric Constructions 29. A ______________ divides a segment or angle in half.
Student Name: Tools of Geometry Module Review 30. A line that intersects a segment at right angles while dividing the segment in half is called a ________.
31. How does a geometric construction differ from a drawing?
32. Is it possible to have a bisector that is not perpendicular to the segment that it bisects? Explain.
Congruent Constructions 33. The picture represents a final step used in...
34. ___________________ lines intersect at a right angle.
Student Name: Tools of Geometry Module Review 35. Explain how protractors are used in geometric constructions.
36. What is a segment bisector? Explain.
Reasoning through Logic Puzzles 37. Which symbol represents "or" in a truth table?
38. If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q, identifying which variable represents which statement. Then write this statement in symbolic form.
39. If the puppy is tired, then he will sleep. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.
40. Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2?
