5th six weeks exam review

  c – b < a < c + b

** Key word: between **i.e. : between which two number must the value of x lie?

Triangle inequality rule

Between which two numbers must the value of x lie?

EX: 9

x

4

Use the triangle inequality rule: 9 – 4 < x < 9 + 4

Simplify by subtracting on the left and adding on the right

5 < x < 13

EX: 9

x

4

If triangle ABC has sides of lengths 6, 10 and x+3, between which two numbers must the value of x lie?

Set up your inequality ◦ 10-6<x+3<10+6

Simplify◦ 4<x+3<16

Solve for x by subtracting 3 (inverse operation)◦ 1<x<13

Answer: 1 and 13

Example 2

If triangle ABC has sides of lengths 7, 14 and x+4, between which two numbers must the value of x lie?

Set up your inequality ◦ 14-7<x+4<14+7

Simplify◦ 7<x+4<21

Solve for x by subtracting 4 (inverse operation)◦ 3<x<17

Answer: 3 and 17

Example 3.. You try

If triangle ABC has sides of lengths 10, 12 and x-4, between which two numbers must the value of x lie?

Set up your inequality ◦ 12-10<x-4<12+10

Simplify◦ 2<x-4<22

Solve for x by adding 4 (inverse operation)◦ 6<x<26

Answer: 6 and 26

Example 4.. You try

If triangle ABC has sides of lengths 10, 25 and 5x, between which two numbers must the value of x lie?

Set up your inequality ◦ 25-10<5x<25+10

Simplify◦ 15<5x<35

Solve for x by dividing by 5 (inverse operation)◦ 3<x<7

Answer: 3 and 7

Example 5.. You try

If triangle ABC has sides of lengths 6, 18 and x, between which two numbers must the value of x lie?

Set up your inequality ◦ 18-6<x<18+6

Simplify◦ 12<x<24

Answer: 12 and 24

Example 6.. You try

Trapezoids can be composite figures too. 1. Cut the trapezoid into separate shapes &

find area of each individual shape. 2. Add the areas together to find the area of

a trapezoid.

New topic.. Markers down..

Find the area by separating into one rectangle and two triangles.

Rectangle: 10x12= 120 Triangle: ½ (3x10)=15

Total= 120+15+15= 150

Example12

18

10

Find the area by separating into one rectangle and two triangles.

Rectangle: 15x9=135 Triangle: ½ (2x9)=9

Total= 135+9+9= 153

Example 2

19

15

9

Find the area by separating into one rectangle and two triangles.

Rectangle: 11.8 x 7.5= 88.5 Triangle: ½ (1x7.5)=3.75

Total= 88.5+3.75+3.75= 96

Example 3

13.8

11.8

7.5