Inequalities in 2 triangles

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Presentation transcript:

Inequalities in 2 triangles Section 5-7

The Hinge Theorem The hinge theorem works by making the following assumptions 2 sides of both triangles are congruent Does the door or the threshold change size when you open the door? The angle in question (hinge angle) must be between the two known sides The other two angles are harder to visualize Keep it simple The hinge angle must be between 0 and 180 degrees The larger third side is related to the larger angle across from it Last section Now for a picture

The Hinge Theorem A F 67 C B 23 D E

NASTY EXAMPLE 1 Find the range of values for x Track across 15 > 10 60 > 5x – 20 + 20 + 20 80 > 5x 5 5 16 > x Since the variable was on the small side, must use the constraint 15 10 60 5x-20

Nasty Example 1 cont. Constraint Final Answer 5x – 20 > 0 + 20 + 20 + 20 + 20 5x > 20 5 5 x > 4 Final Answer 4 < x < 16

Nasty Example 2 Find the range of values for x 9 > 7 3x + 18 > 90 - 18 - 18 3x > 72 3 3 x > 24 Variable is on larger side Apply the other constraint How many degrees in a triangle? 9 3x + 18 7 90°

Nasty Example 2 cont. Constraint Final Answer 3x + 18 < 180 - 18 - 18 3x < 162 3 3 x < 54 Final Answer 24 < x < 54

Assignment Pg 336 – 337 6 – 14 16 – 18