Pre-Assessment Geometry Vocabulary

Pre-Assessment à Geometry Vocabulary

List everything you know (write a definition, draw a picture, etc.) about each geometry vocabulary term.

WHAT’S MY SIZE?

Activity Goals:

· Determine a unit of measurement for an item and accurately measure the item.

· Explain the reasons for differences in estimating and actual measurements.

1. Look around the classroom for the following items. Estimate the length of the following items, without using any measuring tools, and enter those estimates in the table. Include the unit of measure.

Object / Estimated / Actual / Difference
Whiteboard
Height of the door
Length of your table or desk
Length of an unsharpened pencil
Diameter of a penny

2. Why did you choose the units of measure that you chose? How accurate do you think your measurements are? Support your answer using words.

______

3. Measure the items that you previously estimated. Compare your estimates to the actual measurements. Place your answers in the table. Calculate the difference between the actual and estimated measures. List some possible reasons for the difference between the actual and estimated measures.

______

TRIANGLE CLASSIFICATION

4. These are acute triangles These are not acute triangles

Write a definition for an acute triangle.

______

5. These are right triangles These are not right triangles

Write a definition for a right triangle.

______

6. These are obtuse triangles These are not obtuse triangles

Write a definition for an obtuse triangle.

______

7. These are scalene triangles These are not scalene triangles

Write a definition for a scalene triangle.

______

8. These are isosceles triangles These are not isosceles triangles

Write a definition for an isosceles triangle.

______

9. These are equilateral triangles These are not equilateral triangles

Write a definition for an equilateral triangle.

______

10. Review the triangles given below this table. Place the letter of each triangle in all the appropriate

boxes in the table.

Acute / Obtuse / Right
Equilateral
Isosceles
Scalene

A B C

E F G

11. Can an acute triangle also be scalene? ______Why? ______

______

12. Can a right triangle also be scalene? ______Why? ______

______

13. Can an obtuse triangle also be right? ______Why? ______

______

14. Can an obtuse triangle also be acute? ______Why? ______

______

15. Can a scalene triangle also be isosceles? ______Why? ______

______

16. Can a right triangle also be isosceles? ______Why? ______

______

17. Can an equilateral triangle also be isosceles? ______Why? ______

______

MY FRIEND THE PROTRACTOR

Activity Goals:

· Use a protractor to accurately measure and draw angles, with a precision of ±3 degrees.

· Classify triangles.

18. As a class, practice drawing angles with a precision of ±3 degrees. Use a protractor to draw the following angles: 25º, 72º, 147º, and 90º.

19. Measure and label, to the nearest tenth of a centimeter, each side of the triangles below; put the side length measures on the triangles.

Measure, to the nearest degree, each angle of the triangles; label the angles with their appropriate angle measurements.

A. B.

C. D.

20. Classify each triangle from problem 19 according to the size of the angles of the triangles.

Triangle / Acute, Obtuse, or Right / Equilateral, Isosceles, Scalene
A
B
C
D

YEAH, I’VE GOT AN ALTITUDE!

21.

The perpendicular distance from the base of a triangle to the vertex opposite the base is called the altitude of the triangle. The length BD for each triangle above is the altitude of the triangle.

Measure and label all the sides (in centimeters) and angles (in degrees) in each triangle.

What is the measure of angle ADB in all 3 triangles? ______

What type of triangles are the 3 above? And why do you know this? ______

______

Are there any triangles that do not have an altitude? If true draw them, if not true tell why.

______

22. Triangle ABC is an equilateral triangle with altitude labeled a.

a. What is the length of m? ______

b. What is the length of n? ______

23. Explain how you find the value of the altitude a?

______

24. Find the length of a.

Show your work using words, numbers and/or diagrams.

25. a. Without measuring, what is the measure of angle DBC? ______

b. Without measuring, what is the measure of angle DCB? ______

c. Without measuring, what is the measure of angle CDB? ______

26. From 25 a, b, c, above what are the angle measures of triangle BCD? This type of triangle is often encountered in real world applications and is referred to by the angle measures of the triangle BCD. (The triangle’s name is the answers and order of a, b, c from problem 25 above. )

______

30°-60°-90° Triangles

27. Shown below is a 30°-60°-90° triangle that has a leg of length 1 and the hypotenuse of length 2 units. Call this triangle T1. (Note: many calculator answers are approximations. Do not use your calculator for these problems! Find the exact answer algebraically.)

For any right triangle:

A leg is the name of either of the sides of a right triangle that form the right angle.

A hypotenuse is the name of the side opposite the right angle.

a. What is the name of the process that allows you to
calculate the length of the other leg of this triangle?

______

b. What is the formula? ______

c. Calculate the exact length of the leg labeled x.

Show your work using words, numbers and/or diagrams.

With a partner or a small group (no more than 4 students), examine the characteristics of the 30°-60°-90° triangle you are given. Compare your triangle to T1 find all the numeric values of your triangle and share your results with the class.

28. Now consider the 30°-60°-90° triangle, T2, which has one leg of length 2 units and the hypotenuse of length 4 units.

a. How is this T2 triangle related to the T1 triangle above?

______

b. Calculate the exact length of the leg labeled g. ______

Show your work using words, numbers and/or diagrams.

c. How are the hypotenuses for triangles T1 and T2 related?

______

29. Now consider the 30°-60°-90° triangle, T3, which has a hypotenuse of six and a short leg of three.

a. How is this triangle related to T1?

______

b. Calculate the exact length of the second leg. ______

Show your work using words, numbers and/or diagrams.

c. How are the hypotenuses for triangles T1 and T3 related?

______

30. Now consider the 30°-60°-90° triangle, T4, which has a hypotenuse of eight and a short leg of

four.

a. How is this triangle related to T1?

______

b. Calculate the exact length of the second leg. ______

Show your work using words, numbers and/or diagrams.

c. How are the hypotenuses for triangles T1 and T4 related?

______

31. Fill in the table using your results from 27 - 30.

Table I

Triangle / Length of One Leg / Length of the Other Leg / Length of the Hypotenuse
T1 / 1 / 2
T2 / 2 / 4
T3 / 3
T4 / 4
Tn / n

Practice:

32. You are given a 30°-60°-90° triangle with the shortest leg having a length 38 units. Determine the length of the longest leg and of the hypotenuse. ______

33. The value of X is 30º. What is the length of XY and YZ?

a. XY = ______b. YZ = ______c. measure of angle Z = ____

Show your work using words, numbers and/or diagrams.

FROM THE 60’S

34. Shown here is a 30°-60°-90° triangle that has one leg of length units. The measure of angle A is 60°.

Calculate the length of the other two sides.

Show your work using words, numbers and/or diagrams.

35. Shown here is a 30°-60°-90° triangle that has one leg of length 8 units. The measure of angle A is 60°.

Calculate the length of the other two sides.

Show your work using words, numbers and/or diagrams.

36. Calculate the area of each of the triangles from Table I and record your results in Table II.

The area of a triangle is the number of unit squares that can be contained within the triangle.

Table II

Triangle / Length of the Short Leg / Length of the Long Leg 2 / Process / Area
T1 / 1
T2 / 2
T3 / 3
T4 / 4
Tn / n

37. Use your table to determine the exact area for a 30°-60°-90° triangle with the shortest leg measuring 6 units.

38. a. Compare the linear dimensions (lengths of the sides) of triangles T1 and T2.

______

b. Compare the areas of triangles T1 and T2.

______

39. a. Compare the linear dimensions of triangles T1 and T3.

______

b. Compare the areas of triangles T1 and T3.

______

40. a. Compare the linear dimensions of triangles T1 and T4.

______

b. Compare the areas of triangles T1 and T4.

______

41. Make a conjecture (educated guess) of how the area changes when the linear dimensions are changed. Be specific by giving the exact details of your conjecture.

Test your conjecture by using a 30º-60º-90º triangle with a short side of length 14 units and predict the area compared to the area of T1.

______

Was your prediction correct?

Do you think your conjecture will work with any type of triangle?

How could you “test” your answer to the last question above?

I’M ONLY 45

42. On the grid below is a 45°-45°-90° triangle with legs of length 1 unit. Call this triangle T1.

a. What is the name of the process that allows you to calculate the length of the hypotenuse

of this triangle? ______

b. Calculate the exact length of the hypotenuse of the triangle.

Show your work using words, numbers and/or diagrams.

c. What type of triangle is this? ______

43. On the grid, create a 45°-45°-90° triangle with legs of length 2 units. Call this triangle T2.

a. Calculate the exact length of the hypotenuse of the triangle.

Show your work using words, numbers and/or diagrams.

44. Compare the hypotenuses of T2 and T1? ______

______

45. Create a 45°-45°-90° triangle with legs of length 3 cm. Call this triangle T3.

Calculate the exact length of the hypotenuse of the triangle.

Show your work using words, numbers and/or diagrams.

46. Compare the hypotenuses of T3 and T1? ______

______

47. Create a 45°-45°-90° triangle with legs of length 4 cm. Call this triangle T4.

Calculate the exact length of the hypotenuse of the triangle.

Show your work using words, numbers and/or diagrams.

48. Compare the hypotenuses of T4 and T1? ______

______

49. Fill in Table III using your results from 42 - 48.

Table III

Triangle / Length of Legs (cm) / Hypotenuse
T1 / 1
T2 / 2
T3 / 3
T4 / 4
Tn / n

50. Calculate the area of each of the triangles from Table III and record your results in Table IV.

Table IV

Length of Legs / Process / Area of Triangle
1
2
3
4
n

51. A 45°-45°-90° triangle has an area of 32 square units.

What is the length of the of the triangle’s legs? ______

Show your work using words, numbers and/or diagrams.

52. Given that ∆ ABC is an isosceles right triangle with AB = 1 foot:

a. Without measuring, determine the measure of angle ABC______

b. Without measuring, determine the measure of angle ACB______

c. Without measuring, determine the length of side AC ______

d. Without measuring, determine the length of side BC ______

53. Another name for an isosceles right triangle is a ______triangle.

LENGTHS AND ANGLES PRACTICE PROBLEMS

54. Determine the length of side BC. Write your answer in exact value form. ______

Show your work using words, numbers and/or diagrams.

55. This diagram shows the locations of Towns A, B, and C. A person travels from Town A to Town

B to Town C.

Which is the total distance traveled?

A. 12 miles

B. 15 miles

C. 21 miles

D. 36 miles

56. The perimeter of the square is 36 inches.

The perimeter is the distance around the outside of a shape or figure.

Which is the length of its diagonal (d)?

A. 18 in.

B. in. .

C. 12 in.

D. in

57. The dimensions and shape of a volleyball court are shown in this picture.

Which is the distance of a serve that is hit diagonally (from one corner of the court to the other)?

A. 27.0 meters

B. 20.1 meters

C. 15.6 meters

D. 12.7 meters

58. A 60-inch by 100-inch rectangular gate is strengthened by a diagonal wire, which connects two opposite corners of the gate as indicated in the figure below.

Which is the length of ?

A. 80 in.

B. 116 in.

C. 136 in.

D. 160 in.

59. Ted bought an antenna that is 12 feet high. He attached a support wire as shown.

Which is the length of the support wire?

A. 15 ft.

B. 21 ft.