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

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Last updated 15 days ago
39 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.

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.

Question 7
7.

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 y.

_______


Question 11
11.
Find the value:

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


Question 12
12.

Match the image with the angle relationship it describes...

Draggable itemarrow_right_altCorresponding Item
arrow_right_alt
Vertical angles
arrow_right_alt
arrow_right_alt
arrow_right_alt
arrow_right_alt
Question 13
13.

Match the definition of the angle relationship with the angle relationships it describes...

Draggable itemarrow_right_altCorresponding Item
Two angles that are
adjacent and supplementary.
They form astraight line!
arrow_right_alt
Vertical angles
arrow_right_alt
arrow_right_alt
arrow_right_alt
arrow_right_alt
Question 14
14.

Question 15
15.

Match the example to what type of angle pair it represents.

Key points about parallel lines cut by a transversal (These are your reasons):

Alternate Interior Angles are congruent


Alternate Exterior Angles are congruent


Corresponding Angles are congruent


Same-Side Interior Angles are supplementary


Same-Side Exterior Angles are supplementary



Also
Linear pairs of angles are supplementary


Vertical angles are congruent

Question 16
16.
Find x so given that a || b.

x=_______

What is the reason?
_______

Day 2 2/26/25

Determining Order from Smallest to Largest of Sides of a Triangle

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

Smallest _______
Middle _______
Largest _______
Question 18
18.
List the sides in order from smallest to largest.

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

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

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

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

_______
_______
_______

Determining Order from Smallest to Largest of Angles of a Triangle

Question 23
23.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol
_______
_______
_______
Question 24
24.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol

_______
_______
_______
Question 25
25.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol

_______
_______
_______
Question 26
26.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol
_______
_______
_______
Question 27
27.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol
_______
_______
_______
Question 28
28.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol
_______
_______
_______
Question 29
29.
List the angles in order from smallest to largest.
Use the "$$ \angle $$" symbol
_______
_______
_______

Isosceles and Equilateral Triangles

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
_______
Question 35
35.
Find the value of x
_______
Question 36
36.
Find the value of x
_______
Question 37
37.
Find the value of x
_______
Question 38
38.
Find the value of x
_______
Question 39
39.
Find the value of x
_______
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
How many integer values of x are there so that x, 5, and 8 could be the lengths of the sides of a triangle?
8
5
2
12
1
7
3
13
14
How many integer values of x are there so that x, 12, and 6 could be the lengths of the sides of a triangle?
5
18
6
10
7
3
12
8
19
Supplementary angles
Complementary angles
Linear pairs
Adjacent Angles
Two angles across from each other on
intersecting lines. They are always congruent!
Supplementary angles
Two angles that are
next to each other and
share a common side.
Complementary angles
Any two angles whose sum is 90°
Linear pairs
Any two angles whose sum is 180°
Adjacent Angles
Match the angle pairs with their relationship.
equal 180 together
are the same size
Item 1
Item 2
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles