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Biblioteka

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

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Review

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Day 2 2/26/25

Determining Order from Smallest to Largest of Sides of a Triangle

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Determining Order from Smallest to Largest of Angles of a Triangle

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Isosceles and Equilateral Triangles

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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.

Pitanje 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

Pitanje 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 <

Pitanje 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 <

Pitanje 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 <

Pitanje 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< )

Pitanje 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?

Pitanje 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?

Pitanje 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.

Pitanje 9
9.

Find the value of x.

Pitanje 10
10.

Find the value of y.

Pitanje 11
11.

Find the value:

x= °

m∠P= °

m∠Q= °

m∠R= °

Pitanje 12
12.

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

Stavka koja se može prevućiarrow_right_altOdgovarajuća stavka

arrow_right_alt

Vertical angles

arrow_right_alt

Supplementary angles

arrow_right_alt

Complementary angles

arrow_right_alt

Linear pairs

arrow_right_alt

Adjacent Angles

Pitanje 13
13.

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

Stavka koja se može prevućiarrow_right_altOdgovarajuća stavka

Any two angles whose sum is 90°

arrow_right_alt

Vertical angles

Two angles that are

next to each other and

share a common side.

arrow_right_alt

Supplementary angles

Any two angles whose sum is 180°

arrow_right_alt

Complementary angles

Two angles across from each other on

intersecting lines. They are always congruent!

arrow_right_alt

Linear pairs

Two angles that are

adjacent and supplementary.

They form astraight line!

arrow_right_alt

Adjacent Angles

Pitanje 14
14.

Match the angle pairs with their relationship.

equal 180 together

are the same size

Pitanje 15
15.

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

  • Item 2

  • Item 1

  • Corresponding Angles

  • Alternate Interior Angles

  • Alternate Exterior Angles

  • Same-Side Interior Angles

  • Same-Side Exterior Angles

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

Pitanje 16
16.

Find x so given that a || b.

x=

What is the reason?

Pitanje 17
17.

List the sides in order from smallest to largest.

Smallest

Middle

Largest

Pitanje 18
18.

List the sides in order from smallest to largest.

Pitanje 19
19.

List the sides in order from smallest to largest.

Pitanje 20
20.

List the sides in order from smallest to largest.

Pitanje 21
21.

List the sides in order from smallest to largest.

Pitanje 22
22.

List the sides in order from smallest to largest.

Pitanje 23
23.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 24
24.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 25
25.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 26
26.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 27
27.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 28
28.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 29
29.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

Pitanje 30
30.

Find the value of x

Pitanje 31
31.

Find the value of x

Pitanje 32
32.

Find the value of x

Pitanje 33
33.

Find the value of x

Pitanje 34
34.

Find the value of x

Pitanje 35
35.

Find the value of x

Pitanje 36
36.

Find the value of x

Pitanje 37
37.

Find the value of x

Pitanje 38
38.

Find the value of x

Pitanje 39
39.

Find the value of x