MATHCP Geometry  - Unit 20: Features of Right Triangles
Geometric Sequences and Geometric Mean

1) Define a geometric sequence.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
For the next three problems, determine the factor that is used to find the next term in the geometric sequence, and then find the next three terms in the sequence.

2) 2, 4, 8, 16, 32...

4000 character(s) left

3) 1/3, 1/9, 1/27...

4000 character(s) left

4) –10, 20, –40...

4000 character(s) left

5) Select the geometric sequence.

6) Select the geometric sequence.

7) Select the proportion that represents the geometric mean (x) and its relationship between two positive numbers (a and b).

8) Which formula represents the geometric mean (x) between two positive numbers (a and b)? State the letter of the correct answer.

250 character(s) left

For the next three problems, determine the simplified “radical”. For responses that require non-keyboard symbols, the answers should be expressed in the written form.

9) Simplify.

250 character(s) left

10) Simplify.

250 character(s) left

11) Simplify.

250 character(s) left

For the next three problems, determine the geometric mean for the given numbers. Express the answers for non-perfect squares as simplified radicals.

12) 16, 25

250 character(s) left

13) 8, 20

250 character(s) left

14) 13, 17

250 character(s) left

Right Triangles and Altitudes

15) Theorem 20-A: In a right triangle, if an altitude is drawn from the vertex of the right angle to the hypotenuse, then the two triangles that are formed are ___________ to each other and to the given triangle.

250 character(s) left

16) In the lesson link to “Right Triangles and Altitudes”, triangle XYZ and triangle XTY are shown to be similar through a proof. Now, it’s your turn to complete a proof. Use the proof as a model and write a paragraph proof to show that triangles XYZ and XTZ are similar.

20000 character(s) left



Attachments
There are no attachments
 Attach a File
17) Theorem 20-B: In a right triangle, the measures of the altitude drawn from the vertex of the right angle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse created by the __________ of the hypotenuse and the altitude.

250 character(s) left

18) Apply Theorem 20-B to solve for “b”. State the proportion, and then the answer.

250 character(s) left

19) A land owner wants a good approximation of the width of his stream from point D to point C. At point B, he lays a carpenter’s square (used to make right angles) so that he can sight along BC and BA, and he determines that for right triangle ABD, AD = 9.3 feet and BD = 15.7 feet. What is the length of DC?

250 character(s) left

20) Theorem 20-C: In a right triangle with the altitude drawn to the hypotenuse, the measure of a leg is the __________ __________ between the measure of the hypotenuse and the measure of the segment of the hypotenuse that is adjacent to the leg.

250 character(s) left

For the next two problems, refer to the given information and the diagram below.

21) Answer the following questions about the triangle shown below: (a) What is the name of the hypotenuse of triangle XYZ? (b) What is the name of the hypotenuse of triangle XYT? (c) What is the name of the shorter leg of triangle XYZ? (d) What is the name of the shorter leg of triangle XYT? (e) Write a proportion comparing the hypotenuse and the shorter leg of triangle XYZ and triangle XYT, and then state the missing parts of the proportion shown above.

250 character(s) left

22) If ZY = 50 and TY = 15, and “x” equals the length of XY, which statement is correct to determine the length of XY? State the letter of the correct answer. Be sure to read all four possible answers.

250 character(s) left

For the next two problems, refer to the given information and the diagram below.

23) Answer the following questions about the triangle shown below: (a) What is the name of the hypotenuse of triangle XYZ? (b) What is the name of the hypotenuse of triangle XZT? (c) What is the name of the longer leg of triangle XYZ? (d) What is the name of the longer leg of triangle XZT? (e) Write a proportion comparing the hypotenuse and the longer leg of each of the two triangles, and then state the missing parts of the proportion shown above.

250 character(s) left

24) If ZY = 24 and ZT = 8, what is the length of XZ? Round the answer to the nearest tenth.

25) In the figure below, apply Theorem 20-C to determine the lengths of “e”, “f”, and “g”?

250 character(s) left

26) Explain the solutions to the previous problem.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
27) In the figure below, what are the lengths of “a”, “b”, and “c”? Round the answers to the nearest tenth.

250 character(s) left

Pythagorean Triples

28) Explain how the figure below illustrates the Pythagorean Theorem.

20000 character(s) left



Attachments
There are no attachments
 Attach a File
29) Theorem 20-D: If the sum of the squares of the measures of the two legs of a right triangle equals the square of the hypotenuse, then the triangle is a __________ __________.

250 character(s) left

30) Define Pythagorean Triple.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
31) If the legs of a right triangle measure 5 cm and 12 cm, what is the length of the hypotenuse? Do the measurements of the three sides of the triangle form a Pythagorean Triple? Explain why or why not.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
32) If the legs of a right triangle measure 5 ft and 10 ft, what is the length of the hypotenuse? Do the measurements of the three sides of the triangle form a Pythagorean Triple? Explain why or why not.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
33) In the unit link to “Pythagorean Triples”, a formula is provided to generate Pythagorean triples. What Pythagorean Triple would be generated if m = 5 and n = 6?

250 character(s) left

45-45-90 Right Triangle

34) Theorem 20-E: In a 45-45-90 right triangle, the length of the hypotenuse can be determined by multiplying the leg times __________.

250 character(s) left

35) Answer the following questions about the triangle shown below: (a) Explain how you know that the given triangle is a 45-45-90 right triangle. (b) Without using the Pythagorean Theorem, determine the length of the hypotenuse. Round the answer to the nearest tenth. (c) Explain how to determine the length of the hypotenuse using Theorem 20-E.

4000 character(s) left



Attachments
There are no attachments
 Attach a File
36) In the square shown below, what is the length of one side (x)? Round the answer to the nearest tenth.

250 character(s) left

A baseball diamond is actually a square. A model of a professional baseball field is shown below. The baseball diamond measures 90 feet on each side of the square. Refer to the figure below to answer the next three questions.

37) What is the distance from second base to home plate? Round the answer to the nearest tenth.

250 character(s) left

38) What is the distance from the end of the third base foul line to the end of the first base foul line? Round the answer to the nearest tenth.

250 character(s) left

39) The answer to the previous problem can be determined by multiplying 330 feet times the square root (2).

30-60-90 Right Triangle

40) Theorem 20-F: In a 30-60-90 right triangle, the length of the hypotenuse is __________ as long as the shorter leg and the longer leg equals the shorter leg multiplied by __________.

250 character(s) left

41) Answer the following questions about the triangle below, (a) What is the length of segment QS? (b) What is the length of segment QR? Round the answers to the nearest tenth, if necessary.

250 character(s) left

42) In equilateral triangle TRS, find the length of the altitude (PT). Explain and justify the solution.

20000 character(s) left



Attachments
There are no attachments
 Attach a File
43) What is the length of “x”?

250 character(s) left

44) When the six vertices of a regular hexagon are connected with line segments, six equilateral triangles are formed. Segment NM is a perpendicular bisector of the two sides of the hexagon that it touches. What is the length of NM?

250 character(s) left

45) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.
No offline activities found
0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.



Attachments
There are no attachments
 Attach a File