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7.4 Triangle Inequality Theorem (Due 4/25/24)

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34 questions
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Essential Question: How can you use inequalities to describe the relationships among side lengths and angle measures in a triangle?



Learning Target: Students will be able to describe the relationships among triangle sides using side lengths and measures and use that information to solve real-world problems.



Complete the entire document and use full sentences when prompted for full credit.

Responses without work will receive no points.

Question 1
1.

Determine if each group of three side is a triangle.

Triangle
Not a Triangle
16 m, 21 m, 39 m
18 in, 6 in, 13 in
34 km, 27 km, 58 km
29 ft, 38 ft, 9 ft
12 cm, 12 cm, 25 cm
31 yd, 14 yd, 19 yd
Question 2
2.
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

14 and 22

a) Set up difference and sum that shows the possible range of side lengths for the third side

_______ - _______ <third side (x) <_______ +_______

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

_______ < x <_______
Question 3
3.
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

31 and 28

a) Set up difference and sum that shows the possible range of side lengths for the third side

_______ - _______ <third side (x)<_______ +_______

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

_______ < x <_______
Question 4
4.
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

24 and 7

Write the inequality the shows the range of lengths that could be a third side this triangle:

_______ < x < _______
Question 5
5.
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

8 and 17

Write the inequality the shows the range of lengths that could be a third side this triangle ( use <x< )

_______
Question 6
6.

How many integer values of x are there so that x, 5, and 8 could be the lengths of the sides of a triangle?

Question 7
7.

How many integer values of x are there so that x, 12, and 6 could be the lengths of the sides of a triangle?

Question 8
8.
A plot of land is in the shape of rhombus ABCD. If you had to build a fence from point A to C, What is the largest fences you might need to build? Round your answer to the nearest meter._______

If the fencing you have to use costs 45 dollars for each meter. What is the most money you might need to spend to build the fence? Round your answer to the nearest dollar. _______

Review

Question 9
9.

Find the value of x.


Question 10
10.
Find the value of x.

_______


Question 11
11.
Find the value:

x=_______ °
m∠P=_______ °
m∠Q=_______ °
m∠R=_______ °


Day 2 4/25/24

Question 12
12.
List the sides in order from smallest to largest.

_______
_______
_______
Question 13
13.
List the sides in order from smallest to largest.

_______
_______
_______
Question 14
14.
List the sides in order from smallest to largest.

_______
_______
_______
Question 15
15.
List the sides in order from smallest to largest.

_______
_______
_______
Question 16
16.
List the sides in order from smallest to largest.

_______
_______
_______
Question 17
17.
List the sides in order from smallest to largest.

_______
_______
_______
Question 18
18.
List the angles in order from smallest to largest.

_______
_______
_______
Question 19
19.
List the angles in order from smallest to largest.

_______
_______
_______
Question 20
20.
List the angles in order from smallest to largest.

_______
_______
_______
Question 21
21.
List the angles in order from smallest to largest.

_______
_______
_______
Question 22
22.
List the angles in order from smallest to largest.

_______
_______
_______
Question 23
23.
List the angles in order from smallest to largest.

_______
_______
_______
Question 24
24.
List the angles in order from smallest to largest.

_______
_______
_______

Isosceles and Equilateral Triangles

Question 25
25.
Find the value of x
_______
Question 26
26.
Find the value of x
_______
Question 27
27.
Find the value of x
_______
Question 28
28.
Find the value of x
_______
Question 29
29.
Find the value of x
_______
Question 30
30.
Find the value of x
_______
Question 31
31.
Find the value of x
_______
Question 32
32.
Find the value of x
_______
Question 33
33.
Find the value of x
_______
Question 34
34.
Find the value of x
_______