Academic Worksheet 10.1

Academic Triangle Theorem Worksheet
Determine if it is possible to form a triangle with the given side lengths. If not, explain why not.
1.
2 mm, 2 mm, 8 mm 2.
7 yd, 8 yd, 9 yd 3.
15 in., 12 in., 2 in.
4.
18 m, 20 m, 30 m 5.
5 ft, 5 ft, 10 ft 6.
7 mm, 5 mm, 14 mm
Given are the lengths of two sides of a triangle. Find the range of lengths for the third side.
7.
12 cm, 5 cm
10.
7 ft, 13 ft
8.
11.
10 m, 13 m
9 in., 7 in.
9.
12.
7 mm, 4 mm
5 yd, 10 yd
Multiple Choice. Circle the correct answer choice.
13.
Which of the following is false? 14.
A triangle has one angle that measures 61 a.
b.
c.
d.
A triangle can be drawn with more than one acute angle.
A triangle can be drawn with exactly one acute triangle.
A triangle can be drawn with exactly one obtuse angle.
A triangle can be drawn with exactly one right angle.
15.
In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches. Which of the following could be the length of side AC? a.
16 inches b.
5 inches c.
32 inches
16.
degrees, one angle that measures 44 degrees, and one angle that measures 75 degrees. What kind of triangle is it? a.
equilateral triangle b.
acute triangle c.
obtuse triangle d.
right triangle
A triangle has 2 angles that each measure 71°.
What kind of triangle is it? a.
b.
c.
d.
right triangle isosceles triangle obtuse triangle equiangular triangle d.
29 inches
17.
In triangle ABC, the length of side AB is 18 inches and the length of side BC is 26 inches.
Which of the following could be the length of side AC? a.
46 inches
18.
In triangle ABC, the length of side AB is 12 inches and the length of side BC is 21 inches.
Which of the following could be the length of side AC? a.
7 inches b.
49 inches c.
31 inches d.
6 inches
19.
21.
23.
How many triangles exist with the given angle measures? 60°, 60°, 60° a.
b.
c.
a.
b.
c.
No triangle exists
Exactly one unique triangle exists
More than one triangle exists
How many triangles exist with the given side lengths? 3 cm, 5 cm, 9 cm
No triangle exists
Exactly one unique triangle exists
More than one triangle exists
How many triangles exist with the given side lengths? 12 in, 15 in, 18 in a.
b.
c.
No triangle exists
Exactly one unique triangle exists
More than one triangle exists b.
35 inches c.
18 inches d.
38 inches
20.
How many triangles exist with the given angle measures? 55°, 45°, 90° a.
Exactly one unique triangle exists. b.
No triangle exists. c.
More than one triangle exists.
22.
How many triangles exist with the given side lengths? 7 in, 7 in, 7 in a.
More than one triangle exists b.
Exactly one unique triangle exists c.
No triangle exists
24.
How many triangles exist with the given side lengths? 4 m, 4 m, 7 m a.
Exactly one unique triangle exists b.
More than one triangle exists c.
No triangle exists

Academic Worksheet 10.2

Academic Worksheet 10.3

Academic Worksheet 10.4
Find the circumference of the circle. Use 3.14 for π. Round to the nearest whole number.
1.
2.
3.
For a circle with the given circumference 𝐶 , find the radius and diameter of the circle. Round to the nearest whole number.
4.
𝐶 = 63 m 5.
𝐶 = 132 in.
Find the area of the circle. Use 3.14 for π. Round to the nearest whole number.
6.
7.
8.
For a circle with the given area 𝐴 , find the radius and diameter of the circle. Round to the nearest whole number.
9.
𝐴 = 113 cm
2
10.
𝐴 = 7850 m
2
11.
A manhole cover has a diameter of 24 inches. Find the circumference of the manhole to the nearest inch.
12.
The base of a yogurt container has a circumference of about 22 centimeters. Find the radius and diameter of the base to the nearest centimeter.
13.
Find the shaded area of the basketball court to the nearest foot.