# c – b < a < c + b ** Key word: between ** i.e. : between which two number must the value of x lie?

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c – b < a < c + b ** Key word: between ** i.e. : between which two number must the value of x lie?

Between which two numbers must the value of x lie? 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 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

 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

 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

 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

 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

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.

 Find the area by separating into one rectangle and two triangles.  Rectangle: 10x12= 120  Triangle: ½ (3x10)=15  Total= 120+15+15= 150 12 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 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 13.8 11.8 7.5

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