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-Triangle Inequalities. 2.1: Triangle Properties. Spingboard activity. GSE’s.

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-Triangle Inequalities### 2.1: Triangle Properties

Spingboard activity

GSE’s

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts

Th. 5-9:

- If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

1st identify the sides

B

Largest angle

Largest side:

5

Smalles angle

Smallest side:

A

11

7

C

Example 1

- In RGY, RG = 14, GY = 12, and RY = 20. List the angles in ascending order.

Example 2

List the angles in

descending order

1st- Find the side measures

SG=

SB =

BG =

2nd- Use the theorem to order the angles

Largest, middle, smallest angle

Th. 5-10

- If one angle in a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the smaller angle.

B

1st, identify the angles

110

Largest side:

Largest Angle:

C

Smallest Angle:

Smallest Side

2nd, use the theorem to generalize the measures of the sides

20

A

Th. 5.12

Spingboard activity

- The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Th. 5.13- SAS inequality

- If 2 sides of 1 triangle are congruent to 2 sides of a 2nd triangle, and the ___________ of one triangle has a ______ measure than the included angle of the 2nd triangle, then the 3rd side of the 1 Triangle is _____ than the 3rd side of the 2nd triangle.

D

Q

80

4 in

4 in

20

6 in

6 in

E

G

F

A

Th. 5.14: SSS Inequality

If 2 sides of 1 triangle are congruent to 2 sides of a 2nd triangle and the 3rd side in one triangle is _______ than the 3rd side in the 2nd triangle, then the ___________ in one triangle is ______ than the included angle in the 2nd.

I

P

5 cm

8 cm

5 cm

8 cm

E

12 cm

M

W

10 cm

Q

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