Download ExamView - Application with Geometry 3.4

Name: ________________________ Class: ___________________ Date: __________
ID: A
Chapter Three Applications with Geometry Review
1. Find the value of x so the triangle will be equilateral. Then find the perimeter of the triangle.
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2. The perimeter of a triangle is 140 centimeters. The length of the second side is twice the length of
the first side. The length of the third side is ten less than three times the length of the first side.
Find the side lengths and then classify the triangle by the side lengths.
2
2
2
a. 46 cm, 46 cm, 46 cm;
c. 28 cm, 56 cm, 56 cm; isosceles
3
3
3
equilateral
b. 25 cm, 50 cm, 65 cm; isosceles
d. 25 cm, 50 cm, 65 cm; scalene
3. The ratio of the side lengths of a triangular sculpture is 5 : 12 : 12 and the perimeter is 58 feet. What
are the side lengths of the sculpture? Classify the sculpture by its side lengths.
4. The ratio of the angle measures of a triangle is 2 :4 :6 . Find the angle measures and then classify
the triangle by its angle measures.
Find the value of x. Then classify the triangle by its angle measures. (The figure may not be
drawn to scale.)
____
____
5.
a. 41; obtuse
b. 19; acute
c. 20; right
d. 21; obtuse
a. 9; obtuse
b. 10; obtuse
c. 11; acute
d. 20; acute
6.
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Name: ________________________
ID: A
7.
8. Consider the figure shown.
a. Find the value of x. Justify your work.
b. Classify ∆ABC by its angle measures.
c. Find the value of y. Justify your work.
d. Classify ∆ACD by its angle measures.
9. The ratio of the angle measures of a triangle is 1 : 2 : 6.
a. Find the angle measures of the triangle. Justify your answer.
b. Classify the triangle by its angle measures. Justify your answer.
Find the value of x. (The figure may not be drawn to scale.)
____
10.
a. 125
b. 215
c. 80
d. 35
11.
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Name: ________________________
____
ID: A
12.
a. 15
b. 20
c. 30
d. 10
Find the value of x.
____
13.
a. 30
b. 90
c. 25
d. 45
14. Describe the figure using as many of these words as possible: rectangle, trapezoid, square,
quadrilateral, parallelogram, rhombus.
____
15. If all four sides of a parallelogram are congruent, the parallelogram is _______.
a. a nonsquare rectangle
c. a rhombus
b. a trapezoid
d. a kite
16. Any quadrilateral which has two pairs of parallel sides is a ___?___
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Name: ________________________
ID: A
What name best describes the quadrilateral?
____
17.
a. kite
b. rectangle
c. parallelogram
d. rhombus
Performance Task:
18. Draw a Venn diagram showing the relationships among the various types of quadrilaterals.
19. Consider a parallelogram and a rectangle.
a. How do you know if a parallelogram is a rectangle?
b. Draw a parallelogram that is not a rectangle.
c. Can you draw a rectangle that is not a parallelogram? Explain why or why not.
d. Can a rectangle be defined as having two right angles and one pair of opposite sides parallel?
Justify your answer.
20. Describe the difference between a polygon and a regular polygon. Are parallelograms regular
polygons? Explain.
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ID: A
Chapter Three Applications with Geometry Review
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
x = 5 units, perimeter = 72 units
D
10 ft, 24 ft, 24 ft; isosceles
30º, 60º, 90º; right
C
B
92; obtuse
a. The sum of the measures of the angles in a triangle equal 180º; 4x + 52 = 180; x = 32
b. obtuse
c. The sum of the measures of the angles in a triangle equal 180º; (32 + 9) + 52 + y = 180; y = 87
9.
10.
11.
12.
13.
14.
15.
16.
17.
d. acute
a. Since the ratio of the angle measures of the triangle are 1 : 2 : 6, you can write the angle
measures as x°, 2x°, and 6x°. The sum of the angle measures in a triangle is 180º, so x° + 2x° + 6x°
= 180º. Solving for x, you find x = 20. Substituting 20 for x in the above ratio, you find the
measures of the other two angles in the triangle to be 40º and 120º.
b. Since one of the angles in the triangle is greater than 90º, the triangle is an obtuse triangle.
A
24
A
D
rectangle, quadrilateral, parallelogram
C
parallelogram
C
18.
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ID: A
19. a. If the parallelogram has 4 right angles, it is also a rectangle.
b. Sample answer: see diagram below.
c. No. Rectangles have 4 right angles, which makes the pairs of opposite sides parallel.
d. No; Sample answer: The trapezoid below meets the description but is not a rectangle.
20. The sides of a polygon can have any length and the angles all different measures. All the sides of a
regular polygon have the same length and all the angles have the same measure. Squares, which are
parallelograms, are regular polygons. They are the only parallelograms with equal sides and equal
angles. There are not any other parallelograms that are regular polygons.
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