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Geometry Video Notes (5.6/5.7), Triangle Inequality & Hinge Thrm.

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hello Irene this is mistress on Tiana for our geometry class students we are flipping 516 5.7 we couldn't get to it in class the topic here is going to be the triangle inequality theorem in the hinge theorem so here alright let's start off with  the triangle inequality theorem theorem 5.6 obviously has to do triangles going to look at some new relationships with triangles so focusing here there we go so what are we have if we have the following theorem the sum of any two sides of a triangle is longer than the third side no matter what so we have a triangle ABC here and let's make sure we think of triangle ABC as a triangle where this this side and that side are all different measurements so that means that we're looking at the following a b right Plus BCS when it's going to be greater than the third side AC and move it around also a bee plus this bottom base here AC is going to be greater than DC Audio BC list plus AC will always be greater than a be so these relationships is this is the triangle inequality theorem all right let's keep moving on we have theorem 5.7 this is the hinge theorem here's your if statement and it states the following is miserable is turn the measure of angle X then we have that BC is greater than YZ take a look at a picture behind this is what we have we have triangle ABC over here we have XYZ over there notice that is the same as XY same as Z they're saying if measure of angle a angle is greater than measure X which over here you can see is an acute angle then BC this side is going should be greater or longer than YZ  and that's because angle with side BC correspond to each other across from each other and this triangle angle X inside YZ correspond to each other cuz they are across from each other and this is how they are it will take a look at another theorem very similar to this concept to the community room this is an Infamous no Nami known into the serum steering 5.11  and here is a picture  what's we have triangle ABC notice that angle a and angle B are two different angles notice that angle a is obtuse oh it's greater than angle because ingleby is an acute what is an angle a corresponds with side BC right angle be across from they would correspond with Inglewood AC here Serum is greater than measure of angle B that's true you can see that then we have the following B is going to be greater than AC works in within one triangle in the hinge we looked at the comparison of sides and angles in two different triangles let's take a look at the converse now of the hinge theorem theorem 5.14 side side side inequality okay we have two triangles let's compare them triangle ABC triangle XYZ triangle ass this angle inside measurement that correspond with each other a is a straight across the side of bcx angle X across the side crazy ex-wife and AC equals x over the relationship if BC is greater than YZ and you can see that this is a much longer length than it is here then we have the following then we have that measurement Google is going to be greater than the measurement of angle X and we can see that as we explained earlier except when looking at the converse

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Geometry Video Notes (5.6/5.7), Triangle Inequality & Hinge Thrm.

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