Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Can you please answer this worksheet...Please and Thank you so much
![VAT
Geometry 2020-21
Mr Fărzäd
Problem Set [ 09 ]
Name
Per.
Date
Score
Directions: Use a separate sheet to complete the work. Show all diagrams, explanations and related
work in pencil. Label the top of your paper with the correct name and each problem clearly. Scan
to PDF and submit on the appropriate Canvas Assignment.
1. State the definition of a rhombus and one property which applies only to a rhombus but not to any other
parallelogram.
2. The diagram shows rectangle RU ST. Show your work and justify answers using the properties of rectangles.
R
T
(a) Let UY
2x – 1 and RS
3x + 1. Find the value of x.
(b) Find the length of TU based on your answer in (a).
(c) Now, let SU = 6 to find ST based on your answer in (b).
U
S
3. Write the formula for finding the total sum measure of all interior angles of a polygon.
(a) Find the total sum measures of interior angles for polygons with six, twelve, and twenty-four sides.
(b) Suppose the polygons in (a) are regular. Now find the measure of each interior angle for those polygons.
(c) If each interior angle of a regular polygon measures 160°, how many sides does this polygon have?
4. The measure of a single interior angle in a regular polygon is given below. Classify it by number of sides.
(a) 108°
(b) 90°
(с) 135°
(d) 150°
(е) 60°
5. Sketch one concave and one convex pentagon. Check to see if the sum of the interior angles of the concave
pentagon is the same by splitting it into triangles.
6. Three coordinates for the vertices of a parallelogram are given as (5, 2), (8, 6), (–5, 2). Find the coordinates
of the fourth vertex.
(a) Confirm this is a parallelogram using slope. Explain why this confirms it is a parallelogram.
(b) Now, use the midpoint of the diagonals to confirm it is a parallelogram. Explain how the midpoint of
the diagonals confirms this is a parallelogram.
7. Find the area of a regular decagon with apothem 9 inches.
8. List three ways to prove that a given quadrilateral is a parallelogram. Then make a sketch for each situation.
9. The shorter diagonal of a rhombus is 48 mm and the length of the sides are 40 mm. Find the area of the
rhombus. Make a sketch and show all your work. Then, use trig ratios (SOHCAHTOA) to find the interior
angle measures.
10. What is the proper name for the perimeter of a circle? Write the formula in two different ways.
11. The area of a circle is 141.37 sq. yards. Find the radius and diameter of the circle.
12. In the figure with OK, let mLAKE =
Find the following arc measures and classify
each as minor, major, or semicircle.
40°.
AT
D
(а) тAD
(b) тDSA
(с) тEAD
K
E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F276865ef-0fa7-4b36-8f05-381e3e2fbe45%2F0c1c95fa-c160-4072-aa5c-fef126e7b343%2Fyq6fhk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:VAT
Geometry 2020-21
Mr Fărzäd
Problem Set [ 09 ]
Name
Per.
Date
Score
Directions: Use a separate sheet to complete the work. Show all diagrams, explanations and related
work in pencil. Label the top of your paper with the correct name and each problem clearly. Scan
to PDF and submit on the appropriate Canvas Assignment.
1. State the definition of a rhombus and one property which applies only to a rhombus but not to any other
parallelogram.
2. The diagram shows rectangle RU ST. Show your work and justify answers using the properties of rectangles.
R
T
(a) Let UY
2x – 1 and RS
3x + 1. Find the value of x.
(b) Find the length of TU based on your answer in (a).
(c) Now, let SU = 6 to find ST based on your answer in (b).
U
S
3. Write the formula for finding the total sum measure of all interior angles of a polygon.
(a) Find the total sum measures of interior angles for polygons with six, twelve, and twenty-four sides.
(b) Suppose the polygons in (a) are regular. Now find the measure of each interior angle for those polygons.
(c) If each interior angle of a regular polygon measures 160°, how many sides does this polygon have?
4. The measure of a single interior angle in a regular polygon is given below. Classify it by number of sides.
(a) 108°
(b) 90°
(с) 135°
(d) 150°
(е) 60°
5. Sketch one concave and one convex pentagon. Check to see if the sum of the interior angles of the concave
pentagon is the same by splitting it into triangles.
6. Three coordinates for the vertices of a parallelogram are given as (5, 2), (8, 6), (–5, 2). Find the coordinates
of the fourth vertex.
(a) Confirm this is a parallelogram using slope. Explain why this confirms it is a parallelogram.
(b) Now, use the midpoint of the diagonals to confirm it is a parallelogram. Explain how the midpoint of
the diagonals confirms this is a parallelogram.
7. Find the area of a regular decagon with apothem 9 inches.
8. List three ways to prove that a given quadrilateral is a parallelogram. Then make a sketch for each situation.
9. The shorter diagonal of a rhombus is 48 mm and the length of the sides are 40 mm. Find the area of the
rhombus. Make a sketch and show all your work. Then, use trig ratios (SOHCAHTOA) to find the interior
angle measures.
10. What is the proper name for the perimeter of a circle? Write the formula in two different ways.
11. The area of a circle is 141.37 sq. yards. Find the radius and diameter of the circle.
12. In the figure with OK, let mLAKE =
Find the following arc measures and classify
each as minor, major, or semicircle.
40°.
AT
D
(а) тAD
(b) тDSA
(с) тEAD
K
E
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