warm-up: find the missing side lengths and angle measures this triangle is an equilateral triangle...

Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 10 feet 10 feet 25 feet 25 feet This triangle is an isosceles triangle Date: Topic: Triangle Inequalities (6.2) 124

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Warm-up: Find the missing side lengths and angle measures

This triangle is an equilateral triangle

10 feet10 feet

10 feet

12425 feet 25 feet

This triangle is an isosceles triangle

Date:Topic: Triangle Inequalities (6.2)

Page 2: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

Side – Angle RelationshipsIn a triangle, the larger angle is opposite the longer side.

List the angles from smallest to largest:

The smallest side is is opposite

is the smallest angle.

The next biggest side is is opposite

is the next biggest angle.

The largest side is is opposite

is the largest angle.

From smallest to largest: , ,

Page 3: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

Side – Angle RelationshipsIn a triangle, the longer side is opposite the larger angle.

List the sides from shortest to longest:

The smallest angle is is opposite

is the shortest side.

The next largest angle is is opposite

is the next longest side.

The largest angle is is opposite

is the longest side.

From shortest to longest: , ,

Page 4: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

Can a triangle have sides with lengths 1 in, 2 in, and 5 in?

5 inch side

1 inch side 2 inch side

Triangle Inequality TheoremThe sum of the lengths of any two sides of a

triangle is greater than the length of the third side.

2 + 1 = 3 3 < 5

We cannot have a triangle with lengths 1 in, 2 in, and 5 in.

Page 5: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

Determine if the given measure can be lengths of a triangle:

4 cm, 5 cm, 6 cm? 8 cm, 12 mm, 4 cm?

AB BC AC?

The Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

4 cm + 5 cm > 6 cm

YES, since it works for all comparisons

cm?1.2

8 cm > 1.2 cm + 4 cm

NO, since it doesn’t work for this comparison

5 cm + 6 cm > 4 cm4 cm + 6 cm > 5 cm

Page 6: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

Find the range of values for s for the given triangle.

s + 4 > 7

Answer: The length of s is greater than 3 and less than 11

s + 7 > 4

7 + 4 > s

so, s > 3

so, s > –3 (not valid because lengths of sides must be positive)

so, s < 11

Combine the two valid statements:

3 < s < 11

- 4 - 4

- 7 - 7

Page 7: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

We need to find the size of the third angle:

Compare the lengths of the sides of the following triangle. List the sides from longest to shortest.

A 30 65 180A 95 180

A 180 95A 85

85°

List the sides from longest to shortest:

BC , AB , AC

Page 8: Warm-up: Find the missing side lengths and angle measures This triangle is an equilateral triangle 10 feet 25 feet This triangle is an isosceles triangle

In triangle ABC, AB = 9 cm, BC = 16 cm and AC = 24 cm. List the angles of the triangle in order from largest to smallest.

List the angles from largest to smallest:

B , A , C

9 cm

16 cm

24 cm

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